(navigation image)
Home American Libraries | Canadian Libraries | Universal Library | Community Texts | Project Gutenberg | Children's Library | Biodiversity Heritage Library | Additional Collections
Search: Advanced Search
Anonymous User (login or join us)
Upload
See other formats

Full text of "Mechanical drawing; working drawings"

"^.^ 



'I 



university of 

Connecticut 

libraries 




T 353.B12 
Mechanical drawing; 



hbl, stx 



3 T1S3 DDSMTfiMh b 



w -i 



Digitized by the Internet Archive 
in 2013 



http://archive.org/details/mechanicaldrawinOObabb_0 



MECHANICAL DRAWING 



WORKING DRAWINGS 



BY 
ARTHUR B. BABBITT 

TEACHER OF MECHANICAL DRAWING, MANUAL TRAINING 
DEPARTMENT, HARTFORD, CONN., PUBLIC HIGH SCHOOL 




NEW YORK 

HENRY HOLT AND COMPANY 

1911 




^\\z> 



"\ 



^-J 



Copyright, 1911 

BY 

HENRY HOLT AND COMPANY 



PREFACE 

This book is designed to cover two different fields. 
As an elementary text-book it is complete in itself 
and should enable the student to make or read any 
simple mechanical drawing. As an introductory 
work, in schools that offer a three or four years' 
course in Mechanical Drawing, it should lay a good 
foundation for the subject of Projection. 

The drawing instruments are explained as they 

_, are introduced in the course, instead of in a chapter 
by themselves. Each problem is fully discussed 
before the student is expected to attack it. It is 
suggested that the student be required to work out 
his problem for each plate, free-hand, outside of the 
class-room. This will give him valuable practice in 

^xTft'ee-hand sketching, and it will save time in the 

i class-room for needed attention to technique. 

The exercises in lettering (Chapter XIV), should 

Jshow results in the improved appearance of all 
drawings made. The Geometrical definitions are 
usually wanting in books on Mechanical Drawing; 
but are inserted here (Chapter XIV). Even if not 
set as a lesson to be learned, they will still be found 
very useful for reference. The geometrical exercises 

p. in Chapter X\TI are accompanied either by a ref- 
erence to the solution of the problem given in Chap- 



iv PREFACE 

ter XVI, or by the note "original," signifying that 
the student is to work out the problem for himself. 

The course may be given without home-work, but 
the author is a firm believer in home-work. Where 
such work is required, the results immediately aimed 
at are better, and in many indirect ways the subject 
is found to have a higher educational value. The 
author has, therefore, been rather liberal in sugges- 
tions for outside work, and has added extra plates 
for the special benefit of the ambitious student. 

The book represents the work of a year, two 
forty-five minute periods a week, and is the result 
of a ten years' testing process in the class-room,, 
with high school students in the regular course, and 
with young machinists in evening classes. 

A. B. B. 
Hartford, Conn. 

Aug. 15, 1911. 



CONTENTS 



CHAPTER PAGE 

I Material 1 

II Preparation and Use of Material 7 

III Laying out the Sheet 10 

IV Use of Instruments 15 

V Use of Triangles 24 

VI Working Drawings 31 

VII Objects with Oblique Surfaces 53 

VIII Assembly Drawings 66 

IX Use of Instruments 80 

X Cylindrical Work 90 

XI Scaled Drawings 110 

XII Sectional Views 119 

XIII Partial Sections 135 

APPENDIX 

XIV Lettering 153 

XV Geometrical Definitions 165 

XVI Geometrical Problems 180 

XVII Geometrical Exercises 196 



INDEX TO PLATES 



PAGE 

Plate 1 18 

Extra Plate 21 

Plate 2 29 

Plate 3 48 

Extra Plate 51 

Plate 4 56 

Extra Plate 59 

Plate 5 61 

Plate 6 65 

Plate 7 69 

Extra Plate 74 

Extra Plate 77 

Plate 8 82 

Extra Plate 86 

Extra Plate 88 

Plate 9 95 

Extra Plate 98 

Plate 10 100 

Extra Plate 107 

Plate 11 112 

Extra Plate 117 

Plate 12 126 

Extra Plate 132 

Plate 13 143 

Extra Plate 147 



CHAPTER I 

MATERIAL 

An elaborate equipment is not necessary for good 
work in mechanical drawing, but serviceable material 
which with careful handling will produce accurate 
results is required. The list given below covers all 
that is needed to solve almost any problem, and is 
illustrated fully in Fig. 1. 

Drawing-board Ink and pencil erasers 

T square Pencil-sharpener 

Triangle, 30°-60° Thumb tacks 

Triangle, 45° Bottles of drawing ink, red 

Scale and black 

Scroll Penholder, writing pens 

Pencils, 3H and 6H Set of drafting instruments 

Drawing-board — The drawing-board should be 
made of soft pine with the left or working edge, the 
one against which the head of the T square is rest- 
ing in. Fig. 1, perfectly straight. Care should be 
taken to use the same side of the board each time, 
and to have the working edge always at the left. 

T square — The T square consists of two parts, 
the head and the blade. The head of the square is 
shown in contact with the left edge of the board in 



2 MECHANICAL DRAWING 



% 



.\^ 



MATERIAL 




Fig. 1, with the blade extending across the paper. 
The blade is used as the ruhng edge. 

30 °-60 ° triangle — The angles formed by the edges 
of this instrument are 30°, 60°, and 
90° as shown in Fig. 2 ; hence the 
name, 30°-60° triangle. Usually 
only one of the angles is used in 
referring to this triangle and it is 
called either a 30° triangle or a 
60° triangle. 

45° triangle — This triangle is isos- 
celes as shown in Fig. 3, having 
the equal angles 45° and the third 
angle 90°. 

Scale — This instrument has U. S. 
standard graduations and is used for laying off dimen- 
sions. It should never be employed as a ruling edge. 
Scroll — The scroll is made in several varieties and 
is used as a ruHng edge for curves where the 
compasses cannot be employed. 
Pencils — The degree of hardness 
of a drawing pencil is shown by 
the number of times the letter H 
appears on the wooden covering, 
or by the numeral that precedes 
the H. The larger the number, 
the harder is the pencil. 
Erasers — That style in which the pencil eraser is 
at one end and the ink eraser at the other is best, 
simply because it reduces the number of articles on 
the drawing table. 




Fig- 3 



4 MECHANICAL DRAWING 

Pencil-sharpener — Either a pencil file or block of 
sandpaper is necessary for sharpening the lead of 
the pencil. The former is preferable. 

Thumb-tacks — Thumb-tacks with small heads 
should be selected, as they interfere less with the 
movement of the T square. 

Drawing ink — An opaque, waterproof ink, one 
made especially for the purpose, should be used. 
Writing fluids are not suitable. 

Penholder — The diameter of the penholder should 
be small in order that it may enter the small neck 
of the bottle in which drawing ink is usually furnished. 

Writing pens — The ball point style of pen is best 
for lettering, as it is possible to get lines of approxi- 
mately the same width whether making horizontal 
or vertical strokes. 

The set of drafting instruments — While expensive 
instruments are not necessary, instruments with 
which accurate work may be done are essential. 
Should the student decide to purchase a set, the 
selection should be intrusted to one having had ex- 
perience in their use. 

A set of instruments complete enough for any 
draftsman is shown in Fig. 4. 

The compass (A) used for drawing circles and arcs 
either with pencil or ink, is shown with the pencil 
attachment (B) in place. By loosening the clamp- 
ing screw (C) the pencil attachment may be removed 
and the pen attachment (D) inserted. 

The dividers (E) are used for dividing lines into 
a given number of equal parts also for transferring 



MATERIAL 5 

measurements from one part of a drawing to an- 
other. 

The lengthening bar, shown at G, has a projection 




at one end to be inserted in the leg of the compass, 
and a receptacle at the other end into which either 
the pencil or pen attachment may be placed. This 
extension is used when circles of large radii are desired. 



6 MECHANICAL DRAWING 

Two sizes of straight-line pens are shown at H, 
either of which may be used, the selection being left 
to the workman. 

Instruments K, L, and M are called bow instru- 
ments, K being the bow pencil, L the bow pen, and 
M the bow dividers. With these instruments small 
work may be executed more accurately than with 
the larger instruments. 

N is a cylindrical tube used for holding leads for 
compasses. 



CHAPTER II 

PREPARATION AND USE OF MATERIAL 

The pencils — To do good work, one must keep 
all pencils sharp; and to keep pencils sharp requires 
constant attention. The 6H pencil is to be sharp- 
ened at both ends; the 3H should be sharpened at 
one end only. To sharpen the pencil, remove the 
wood exposing about three-eighths of an inch of the 
lead, being careful, however, not to let the knife 
edge cut into the graphite. The lead should be 
sharpened by using the pencil sharpener or file. 
One end of the 6H pencil should be sharpened to an 
ordinary round point and the other end to a chisel 
point. To sharpen the round point after removing 
the wood, pass the lead across the file at the same 
time rotate the pencil between the fingers. This 
should give a long, conical point, tapering from the 
place where the wood meets the lead to the extreme 
point, with the end as sharp as a needle. When 
sharpening the chisel point, pass the lead across the 
file without rotating the pencil, tapering the cut from 
the wood to the end and removing the graphite until 
one-half at the end is gone. Repeat this process on 
the reverse side of the lead until the point has been 
brought to a knife edge. The 3H pencil should be 
sharpened to a conical point. 



8 MECHANICAL DRAWING 

The 3H pencil is used for sketching, for printing, 
and for other free-hand work. All of the straight line 
mechanical work on the drawing should be executed 
with the 6H pencil. The round point of the 6H 
pencil is used for locating points and the chisel point 
for drawing lines, with the flat of the chisel against 
the ruling edge. One must early accustom himself 
to changing from the round to the chisel point, and 
vice versa, for different character of work. 

The T square — The T square should always be 
used with the head against the left edge of the board, 
and the upper edge of the blade should always be 
employed as the ruhng edge. All horizontal lines 
should be drawn from left to right, with the T square 
as a guide. The blade of the square should not be 
brought up to the point through which the line is to 
be drawn, but should be so placed that there will be a 
minute space between the blade and the line after 
the line shall have been drawn. 

The triangles — For the vertical lines of the draw- 
ing the 60"" triangle is usually employed, as it 
gives a longer ruling edge than the 45° triangle. 
When used for vertical lines, the triangle should be 
placed on the upper edge of the T square with the 
60° angle at the right, as shown in Fig. 6. The 
placing of the triangle for 30°, 45°, and 60° lines 
will be determined by the direction in which these 
lines are to be drawn. 

The scale — Keep the scale between the body and 
the line upon which the measurement is to be taken, 
thus bringing the instrument under the hand. When 



PREPARATION AND USE OF MATERIAL 9 

laying off dimensions, see that the mark is made 
directly opposite the required graduation on the scale. 
The eraser — For pencil work use only the pencil 
end of the eraser. If this will not do the work, it is 
no fault of the eraser but it is because the pencil 
lines have been made too heavy. Erase in the di- 
rection in which the line is drawn and not across the 
line. To remove a line, use many light strokes rather 
than dig into the paper with a few hard ones. Never 
wet the eraser for either pencil or ink erasing. For 
erasing inked lines use the ink end of the eraser, 
following the directions for erasing pencil lines. Be- 
fore attempting to erase, be sure that the ink is per- 
fectly dry. 



CHAPTER III 
LAYING OUT THE SHEET 

Each drawing should be inclosed within a rec- 
tangle, the lines of which may be called margin lines. 
This, in tm^n, should be inclosed in a larger one called 
the cut-off rectangle the size of the finished sheet. 
The cut-off lines are those upon which the drawing 
is trimmed after being taken from the board. 

When laying out the margin and cut-off lines, 
proceed in the following manner: 

1. Tack the paper to the board with the longest 
edge parallel with the upper edge of the blade of the 
T square. Place the paper nearer the upper than the 
lower edge of the board and nearer the left edge 
than the right. A good way to stretch the paper 
on the board is first to insert a thumb-tack in the 
upper left-hand corner, then, by passing the hand 
across the paper, being careful not to change the 
location of the paper on the board, stretch the upper 
edge and insert a tack in the upper right-hand corner. 
Stretching the left vertical edge, place a thumb-tack 
in the lower left-hand corner. The final stretching 
may be accomplished by passing the hand diagonally 
across the paper from the upper left to the lower 
right, and forcing the last tack into place. Remem- 
ber that the tacks are thumb tacks and should not 



LAYING OUT THE SHEET 



11 



be driven into the board by hammering with a knife 
or T square. 

2. Find the center of the sheet by using intersect- 
ing diagonals from the corners of the paper. See 







; 














■ 


-i- 










-i^ 








/* 


y 






c 


i 




/^cif^i^//^ L /r>e3 






> 




Coit-off L/nes. 



© 



£cf^s of /^c/^sr 



/=/y. S 



point A, Fig. 5. Only that part of the diagonal at 
or near the center of. the sheet needs to be drawn. 
The T square may be used in getting these lines, 
by placing one of the edges of the blade diagonally so 
it will intersect opposite corners of the paper. 

3. Using the scale, measure five inches up and down 
and seven inches to the right and left, locating points. 
Most scales are not graduated to the extreme end, 
and care should be taken to measure from the point 



12 



MECHANICAL DRAWING 



where the graduations begin and not from the end 
of the scale. When locating the points, make a 
very small dash directly opposite the required grad- 
uation on the scale. This mark should be made 
with the round end of the 6H pencil, and should be 
a very light dash and not a point drilled into the 
paper. When using the scale, remember the direc- 
tions, and keep the instrument under the hand. 




Fig. 6 

4. With the head of the T square held firmly 
against the left edge of the board, and using the upper 
edge of the blade as guide, draw, very hghtly, hori- 
zontal lines through the upper and lower points. 
Through the points at left and right draw vertical 
lines, using the 60"' triangle as a ruhng edge. When 
using the triangle for vertical lines, keep the 60° 
angle to the right, as shown in Fig. 6. Unless the 
triangle is a large one, it will be necessary to make 



LAYING OUT THE SHEET 



13 



the line in two parts. Use great care to make the 
Une continuous, without a perceptible joint. 

5. Locate points f ^' above the upper margin line, I" 
to the right of the right-hand margin hne, I" below 
the lower margin hne, and i" to the left of the left- 
hand margin line. 



^/y 7 



/^/^. 3. 



6. Through these points draw lines forming the 
outer rectangle shown in Fig. 5. These lines form 
the finished size of the sheet. 

In Figs. 7 and 8 are shown, respectively, the 
upper right and lower right-hand corners of the draw- 
ing, giving the lines to be drawn for the printing and 
the relation of these lines to the margin lines. The 



14 MECHANICAL DRAWING 

plates should be numbered consecutively, and each 
one should have the draftsman's name and the date 
of finishing the drawing. 



CHAPTER IV 
USE OF INSTRUMENTS 

(Straight Line Work) 
PLATE 1 

SUGGESTIONS FOR PENCILING 

Accuracy and neatness are the two essentials 
for good work in mechanical drawing. As stated 
before, sharp pencils are absolutely necessary to 
do accurate work and should be the first things to 
receive attention when beginning the lesson. Not 
that only once during the lesson should the pencil 
be pointed, but one should begin with the tools in 
proper condition, and then,^ — keep them in condition. 
To do neat work requires clean hands, careful at- 
tention to details, light lines, and painstaking eras- 
ing, when erasures are required. Special attention 
should be given to the making of light, fine lines, for 
heavy lines are a disgrace to any draftsman. Re- 
member that you are making the drawing on the 
paper and not into it. With the hard 6H pencil 
it requires no great pressure to cut a line into the 
paper that no amount of erasing will remove. One 
does not usually err by making the lines too fine and 
light. When using the scale, be careful to make the 
marks directly opposite the required graduations 



16 MECHANICAL DRAWING 

and when drawing the lines, see that they go exactly 
through the points located. All horizontal hnes 
should be drawn from left to right and all vertical 
lines from the bottom up. In general, draw the lines 
away from the body. 

SUGGESTIONS FOK INKING 

The straight-line or drawing-pen — This pen should 
be used for inking all straight lines of the drawing 
and all curves where the scroll is required for the rul- 
ing edge. The thumb-screw is for adjusting the 
nibs of the pen for the different widths of lines. Care 
should be used not to screw this thumb-screw up 
too tight, for the threads are very fine and will 
easily strip off, thus ruining the pen. To fill the 
pen, place the quill — one is usually furnished with 
the small bottles of drawing ink — between the blades 
of the pen near the point, and the ink will readily 
flow from the point of the quill to the space between 
the nibs of the pen. Do not have more than iV of 
ink in the pen, for a larger amount will cause a pres- 
sure at the point with a tendency to blot. Never 
hold the pen or quill over the paper, when filling the 
pen. Before attempting to make a line, see that no 
ink is on the outside of the blades of the pen. If 
there is, clean it off with the pen-wiper. If none is 
furnished with the bottle of ink, a soft cotton cloth 
may be used. Always try the pen outside of the 
cut-off line before starting to ink a drawing, not only 
to see if the pen is working properly, but also to ad- 
just for the proper width of line. If interrupted 



USE OF INSTRUMENTS 17 

while inking a drawing, always see that the pen is 
adjusted to the proper size of Hne, before taking up 
the work again. When it becomes necessary to re- 
fill the pen, the sediment remaining between the nibs 
should be wiped out by passing the pen-wiper be- 
tween the blades. This means that the pen should 
be cleaned each time it is filled. 

Using the drawing-pen — Hold the pen with the 
thumb-screw away from the body, with the end of 
the index finger of the right hand bearing against 
the outside blade just above the 
thumb-screw. Incline the pen 
slightly with the ruhng edge and 
also in the direction of motion. 
The proper relation of pen and 

ruling edge is shown in Fig. 9. 

The distance between the pen point 

and the ruling edge should not be /vy. 3 

too great lest the outer nib of the 

pen be raised from the paper and make a ragged, 

uneven line. 

Erasing mistakes — If a mistake or blot makes it 
necessary to remove some of the inked work, first 
be sure that the ink is perfectly dry. Do not try 
to erase with a few hard strokes, for time and patience 
are necessary essentials to remove lines without 
showing the effect of the erasure. 



PLATE 1 

Follow the directions given on the next pages. 
Work carefully, accurately, and neatly. Keep the 
pencil sharp, using the conical point for locating 
points and the chisel point for drawing lines. Use 
a light, fine line. 

INKING 

When inking, follow this order : 

1. Horizontal lines. Ink those at the top first. 

2. Vertical hues. Ink those at the left first. 

3. Obhque hnes. Ink in the most convenient 
order. 

4. Printing. Use the writing pen. 



DIRECTIONS FOR MAKING PLATE 1 

Locate a point Ire" below the upper margin 
line. Through this point draw a horizontal line 
connecting the left and right-hand margin lines. 
Locate points on this line Iri'' in from each 
vertical margin line. Erase the porti*. n of the line 
between these points and the margin lines. This 
should leave a horizontal line lOF' long. Draw 
two vertical lines extending down from the ends of 
this horizontal line a distance of li'\ Locate 
points Te" apart on the left-hand vertical line. 
Through the first point below the horizontal line, 
draw a dotted horizontal line to the vertical line 
at the right of the figure. Through the next point 
below, draw a full horizontal line. Through the 
next point below, draw a dotted line, and through 
the lowest point draw a full line, completing the 
figure. When drawing the dotted lines, make the 
dashes of equal length and have them equally spaced. 
Dashes should be not more than §'^ nor less than 
A'' long, and the space between dashes should 
equal about i the length of the dash. 

Construct a square having sides 4'^ long, with the 
left side 2" from the left margin line and the lower 
side Ite" from the lower margin line. Using the 
scale, divide the lower side. of the square into four 
equal parts. Through these points draw vertical 



20 MECHANICAL DRAWING 

lines to the upper side of the square. From the 
points where these vertical lines meet the upper side, 
draw 45° lines to the left side of the square. From 
the points on the lower side of the square, draw 45° 
lines to the left side. 

Construct a square having sides 4'^ long, with the 
right side 2" from the right margin line and the 
lower side liV from the lower margin line. Divide 
the upper side of this square into four equal parts. 
Draw vertical Unes across the square through the 
points located. Through the points on the upper 
side of the square draw 45° lines to the right side. 
Through the points where the vertical lines touch 
the lower side, draw 45° lines to the right side. 



EXTRA PLATE 

Draw a 71^^ square in the center of the sheet, 
and copy one of the figures given on pages 22 and 23. 

Note that the figures are determined by first draw- 
ing horizontal and vertical lines across the square 
from points equally spaced on the sides. 

INKING 

The light lines of the figure are to be drawn 
in pencil only; heavy lines are to be inked. When 
inking, follow the order given for Plate 1. 



22 MECHANICAL DRAWING 




No 2 






No. 4. 




No 3 No. Q. 

Plate 1, Extra Plate 



USE OF INSTRUMENTS 



23 



/ 


\ 






d ' 


^^n 


yy 




> ^^ 


/ ^ 


^^ 


[P 






V 


7~ 



No. 7 



No 9. 



/ 


X 


X 


^J 


IN 


X 


X 




X 


A 


X 


"v^ 


X 


X 


X 


X 


y 


A 




\/ 


X 


\ 


X 


X 


X 


> 


> 


X 




X 


X 


X 


X 


X 


X 




X 


< 


X 


tx 


X 


X 




X 


A> 




X 


X 


X 


X 


A 


\ 


^; 


X 




X 




A 


X 


X 


A 


X 




A 



/\ 


\Z S7 


t \^^ ^ 


S ^'^^^N W 


Z\ S^^2\ \^ 


7 /\ ^ Tjs 5 


^ ^t^ V^?^7 


\ ^2="^5 S7 


7\ \^^ S 


\^\7\ 


/\ 7\ 


^z 



No. 3. 



No. lO. 



No. II No. 12 

Plate 1, Extra Plate 





















■ 




X 




X 


\ 


X 


X 












\— 








-1 






X 




X 


X 


X 


k 


\ 
















-l 






1 










X 


/ 


X 


X 


X 


X 


X 














































\ 






/ 


X 


\ 


























X 






\ 


X 


// 




















X 


X 


IX 


X 


X 


/ 


X 


\ 
















1 














X 


X 


K 


X 


k 


X 


X 


/ 













, 






_ 


















~ 


~ 






X 


X 




X 


\ 


X 





r 


X 


\ 




x 


X 


X 


k 


X 


X 


y 


X 


k 


X 


y 




A 


X 

X 


X 


X 








X 


X 


XX 


V 


X 
X 


y 




k 


X 


A 


X 


k 


k 




/ 


X 


^ 


\ 


XX 


X 


^ 


X 


X 


y 

X 


n 


X5^ 


X 


X 


X 


^ 


\ 


XXXTx 


x^ 



CHAPTER V 

USE OF TRIANGLES 

PLATE 2 

On pages 26 and 27 are shown the different ways 
in which triangles may be placed in relation to the 
T square, both singly and in combination. From 
the illustrations it will be seen that angles of 30°, 
45°, and 60° with the horizontal or vertical may be 
obtained by using triangles singly, while for angles 
of 15° and 75° a combination of triangles is necessary. 
When two points are so located that the line con- 
necting the two cannot be drawn with the triangles 
in any of the positions shown on pages 26 and 27, 
the quickest and best method is to place the pencil 
on one of the points with one edge of a triangle 
against the pencil, then, rotating the triangle until 
the same edge coincides with the other point, draw 
the line. 

PARALLELS AND PERPENDICULARS 

For drawing a parallel to a given line through a 
given point, using the triangles, place one edge of a 
triangle on the line with the second triangle bearing 
against one of the other edges of the first triangle. 
Holding the second triangle firmly, slide the first 



USE OF TRIANGLES 25 

one along its edge until it is in the required position. 
In Fig. 10 is illustrated the method whereby a line 
may be drawn through C parallel to M N. The 
long edge of the 45° triangle is made to coincide with 
the given line M N, and the long edge of the 60° 
triangle is placed against one of the short edges of 
the 45° triangle. These positions are shown in full 
lines. From this position the 45° triangle is moved 
along the edge of the 60° triangle until its long edge 
coincides with the point C, or to the position shown in 
dotted lines. The triangle is then in position to 
draw the line X Y, which will be parallel to M N. 

To draw a perpendicular to a given line through a 
given point on or outside of the line, place the tri- 
angles in the same position as for parallels and then, 
rotating the 45° triangle to the position shown in 
dotted lines in Fig. 11, the required perpendicular 
may be drawn. In Fig. 11, the line M N is the given 
line, and X Y the perpendicular through either C or C. 

Another method which may be employed for draw- 
ing the perpendicular is illustrated in Fig. 12. In 
this case the short edge of the triangle is made to co- 
incide with the given Une and is then pushed along 
the edge of the second triangle, thereby bringing the 
other short edge to the point through which the re- 
quired perpendicular is to be drawn. In Fig. 12, 
the line M N is the given line and X Y is the required 
perpendicular through C. 

In Figs. 10, 11, and 12 the 45° triangle was used as 
the first triangle, although the 60° triangle might 
have been used with the same result. Thus in Fig. 13 



26 



MECHANICAL DRAWING 










USE OF TRIANGLES 



27 




28 



MECHANICAL DRAWING 




f^ia 1^- 



we have the same proposition as in Fig. 11, with an 
interchange of triangles. Do not under any consid- 
eration place one edge of the right angle of a tri- 
angle against a line and use the other edge bounding 
the right angle to draw a perpendicular to that line. 
Good, accurate work cannot be done in this way. 



PLATE 2 

Make drawings of the geometrical figures given 
in one of the rectangles shown on page 30. The 
rectangle shown in the copy represents the margin 
lines. 

Keep the pencil sharp, using the conical point for 
locating points and the chisel point for drawing lines. 
Make very light, fine lines. Do not put the dimen- 
sions on the drawing. 

INKING 

Ink only the heavy lines shown in the copy. 
Have the drawing complete in pencil before inking. 
When inking, follow the order given on page 18. 



30 



MECHANICAL DRAWING 




Plate 2 



CHAPTER VI 

WORKING DRAWINGS 

PLATES 3 AND 4 

If we look at an object through a transparent plane 
and trace the outline as seen upon that plane, the 
result is a perspective drawing of the object. The 
relation of the object to the plane determines the 
character of the drawing, and as the observer changes 
his position relative to the plane his view of the ob- 
ject will also change, giving for different positions 
entirely different drawings. 

In perspective drawing all the points of sight pro- 
ducing the outline on the picture plane converge 
to one point, namely the eye of the observer. This 
causes all lines of the object in contact with the pic- 
ture plane to be in their true length in the drawing, 
while all lines back of the picture plane will be short- 
ened. This foreshortening of lines with the in- 
ability to measure them, makes the perspective 
drawing of very little value to the workman. 

In making the working drawing or mechanical 
drawing, we consider that all lines of sight producing 
the picture are parallel to each other, thus giving 
views of lines parallel to the picture plane in their 
true length. In Figs. 14 and 15, page 32, are il- 



32 MECHANICAL DRAWING 




Fig J 4 




WORKING DRAWINGS 33 

lustrated the two principles by which the perspective 
drawing and the working drawing views are ob- 
tained. Note that in Fig. 14 none of the hnes are 
seen on the picture plane in their true length, being 
foreshortened because of the converging lines of 
sight, while in Fig. 15 all the lines of one face of the 
object are seen not only in their true length but also 
in the true relation to each other. 

The perspective drawing gives the general outline 
and relation of parts in one view, while in mechanical 
drawing more than one view is required to clearly 
illustrate an object. Sometimes two views only 
are necessary to show the shape or construction, 
while in other cases three, and occasionally more, 
are required. These two or more views, drawn ac- 
cording to given principles and in the proper relation 
to each other, with enough dimensions for making 
the object represented, constitute a mechanical 
drawing. 

THE THREE VIEWS 

A free-hand perspective drawing of a model from 
which it is required to make the working drawing, 
is given in Fig. 16, page 34. Let us, for convenience, 
call the surface A the front surface of the object, 
B the top surface, and C the side surface. To get 
a view of surface A, we would look in the direction 
indicated by arrows D, shown in Fig. 17. This view, 
being of the front of the object, may be called the 
front view, and may be placed at A, Fig. 18. The 
view of the top surface, or top view, would be ob- 



34 



MECHANICAL DRAWING 




WORKING DRAWINGS 35 

tained by looking in the direction indicated by the 
arrows E. This being the top view, we would most 
naturally place it above the front view, when group- 
ing the views. In Fig. 18, the top view is shown at 
B, directly above the front view. To obtain the 
view of the side of the object, or surface C, we would 
look in the direction indicated by the arrows F, and 
would get the view shown at C, Fig. 18. This be- 
ing the right side view of the object, it is placed at 
the right of the front view. The relation of the three 
views then will be as follows: 

The top view is directly over the front view. 

The side view is directly to the right of the front view. 

A study of the three views given in Fig. 18 shows 
that the height of the front and side views is the 
same, the breadth of the front and top views is equal, 
and that the height of the top view and breadth of 
the side view are identical. From these statements 
we may formulate the following rules: 

1. The vertical dimensions on front and side views 
are equal. 

2. The horizontal dimensions on front and top views 
are equal. 

3. The vertical dimension on the top view equals the 
horizontal dimension on the side view. 

. It is not necessary to use the front face of the ob- 
ject as the front view. Any surface may be employed 
as the front view, provided the other views are drawn 
in the proper relation to this view\ Thus, in Fig. 19, 
the surface C, drawn with its long edge in a horizon- 
tal position, is used as the front view, with surfaces 



36 MECHANICAL DRAWING 

A and B as top and side views, respectively. Still 
another combination is shown in Fig. 20, page 37, 
in which B is the front view, C the side view, and the 
surface across the object from A, which may be called 
A', the top view. In Fig. 21, the front view C in 
Fig. 19 is drawn with its short edge horizontal. This 
causes B to become the top view and A the side view. 
Fig. 22 is the same as Fig. 20, with the top view 
omitted. Notice that these two views show the shape 
and size of the object as well as do the three views 
of Fig. 20. This saves the drawing of the third view; 
but in our practice, for the present, we will draw the 
three views even though they may not be absolutely 
necessary. 

The block shown in Fig. 23, page 38 is the sartie 
as that illustrated in Fig. 16, but with a mortise 
cut into the block on the surface A. Three views 
of this object are given in Fig. 24, in which the sur- 
face A becomes the front view, B the top view, and 
C the side view. The mortise is represented on the 
front view by the inner rectangle, and is expressed 
on the top and side views by dotted lines. Inas- 
much as the mortise is not visible from the top or 
side, some characteristic must be employed to dis- 
tinguish the visible from the invisible edge. Full 
lines are employed to represent visible edges of the 
object, and dotted lines for the invisible edges. These 
lines may be grouped under one head and called 
the main or primary lines of the drawing. 



WORKING DRAWINGS 37 

















A' 
















B 




C 










F 


■is- 2 








B 


















C 




A 








/ 


^j 


7.2/ 


















' 




n 


■g.22 







38 



MECHANICAL DRAWING 




WORKING DRAWINGS 39 



DIMENSIONS 

The drawings we have just considered, while well 
representing the objects, do not give enough in- 
formation for making the models. Not only must 
the general outline, shape, etc., be shown, but the 
dimensions necessary for making the model to a 
definite size must also be given. In Fig. 25 is shown 
the complete drawing of the model illustrated in 
Fig. 24, not only the shape but the sizes as well be- 
ing given. To indicate these dimensions, other 
lines and characters are employed which may be 
grouped under one head and called the secondary 
lines of the drawing. The names of the lines included 
in this secondary group are witness or extension lines, 
and dimension lines. Other characters used are 
arrow-heads. The figures placed on the drawing 
are called dimensions. 

A dimension line is one upon which the dimen- 
sion is placed and in which a break is made for the 
dimension. iVrrow-heads are placed at the extremities 
of this line. A witness or extension line is one extend- 
ing out from the object line to and a little beyond 
the dimension line, employed when the dimension 
is placed outside the view. Different characters 
of lines are used in different drafting rooms for these 
secondary lines, so a system employed in one text 
book could not conform to every drafting-room 
system. For the work in this course, dotted lines 
will be used for witness lines, and a full line, with 
space reserved for the dimension, will be employed 



40 MECHANICAL DRAWING 

for the dimension line. The arrow-head should not 
fall short of or project over the witness or object 
line to which it goes, and should be made shorty 
narrow, and pointed. 



SUGGESTIONS FOR DIMENSIONING 

Place all dimensions possible on one view, but 
give dimensions to full lines in preference to dotted. 

Avoid crossing horizontal and vertical dimension 
lines. 

So place the dimension that it can be erased with- 
out erasing a hne of the drawing. 

Have horizontal dimensions read from the bottom 
and vertical dimensions from the right of the draw- 
ing. See Fig. 25. 

Do not use an oblique line as the vinculum of a 
fraction; make this line par- 

I i I I ! } allel to the dimension line. 

ia 1^ I J / hi Make F^ not 1/8''. Use great 

' ^^ I 11 I I ^ care in making the figures ; 

I I 1 ! 1 1 these are vital parts of the 
^^ ^^ drawing. 

Be sure to have the three di- 



mensions — length, breadth, and thickness— for the 
main piece, also for all projections and recesses. 

When it is impossible, because of the narrow- 
ness of the space, to get both dimensions and arrow- 
heads between the witness lines, the arrow-heads, 
or the dimension, or both, may be placed outside. 
These three methods are shown in Fig. 26. 



WORKING DRAWINGS 



41 



Do not use the " marks, when all dimensions are 
in inches. 



LOCATING THE DRAWING IN THE RECTANGLE 

Unless a drawing is located in the center of the 
rectangle in which it is drawn, the appearance of the 
drawing is marred. It is, therefore, advisable to place 
the views with reasonable spaces between, and with 
equal margins at the top and bottom, also at the 




right and left. The drawing shown in Fig. 27, surely 
is more pleasing to the eye and makes a better im- 
pression than the one shown in Fig. 28. This is 
due entirely to the proper placing of the drawing 
within the rectangle bounding it. 

The exact location of the drawing on the sheet 
should be determined before a line is drawn. This 
may be obtained by finding the full height and width 
of the drawing, including the space between views, 



42 



MECHANICAL DRAWING 



subtracting these dimensions from the height and 
width of the sheet, and dividing the difference by 




two. This will give the spaces at the top and bot- 
tom and the spaces at the right and left. Thus, in 





\ 






^ 






\ 








^ 






\ 




+ 




^^ 






i 














— 2 -* 




— B — 


c^ 






-3'-^ 




^i(\i 
^ 


-/i- 






t 










\ . -. 


1 



Fig. 29 

Fig. 29, the spaces A and A' may be obtained by 
adding the height of the front view, ?>\" , the height 



WORKING DRAWINGS 



43 



of the top view, 2" ^ and the space to be allowed 
between the front and the top views, \" ^ and sub- 
tracting the sum,6i'', from the height of the rectan- 
gle, 9^', leaving the amount to be divided equally be- 
tween A and A^ 2h" . If we 
make A and A' equal, then 
each would be li^^ The 
spaces B and B' may be ob- 
tained in the same manner by 
adding the width of the front 
view, 5i'', the width of the 
side view, 2" ^ and the space 
between views, \^\ making a 
total of ^\" , Subtracting this 
total from the width of the 
rectangle, VI" , and dividing by 
two, we have, VI" -"^h" = Z\" , 




and Z\"-2 = V^'. Therefore 



nj,30 



spaces B and B' should each be made H" . It will be 
noticed in the above illustration that more space was 
allowed between the front and side views than be- 
tween the front and top views. It is not necessary 
that these spaces be equal; in fact it is better under 
certain conditions that they be unequal. In the 
figure we have been discussing, there is more blank 
space horizontally than vertically; therefore there 
should be more space between views horizontally 
than vertically. 

Let us consider one other condition. The drawing 
shown in Fig. 30 is to be placed in a rectangle 9'' 
high and \2" broad. If we should allow V be- 



44 MECHANICAL DRAWING 

tween the front and side views, the total horizontal 
width of the drawing would be 5f\ This sub- 



T/y. 3/ 

tracted from the horizontal dimension of the sheet 
would give 61^' to be divided into two equal parts, 
for the spaces at right and left. These spaces would 
then be SV each. Allowing V between the front 
and top views, the total height of the drawing would 
be 8y\ The difference between this height and the 
height of the rectangle would be i'\ which, divided 
by two, would give }'' each for spaces at the top 
and the bottom of the drawing. A drawing placed 
according to these conditions is shown in Fig. 31. 
One can readily see that there is too much space 
between the top and front views, when we compare 
it with the spaces at the top and the bottom of the 
drawing. If we reduce this space from V to ¥', we 
will then have an additional i'' to be divided 
equally and added to the spaces at the top and the 
bottom, making each of these i'', instead of j' as 



WORKING DRAWINGS 



45 



in the previous case. A drawing made to suit these 
changed dimensions is shown in Fig. 32. Even 




/-/> 32 

though this is an improvement over the other con- 
dition, it still looks awkward with so much space 




horizontally and so Httle vertically. The reason 
for this is that we have been attempting to place the 



46 MECHANICAL DRAWING 

long dimension of the drawing in the short dimension 
of the rectangle. By a rearrangement of views as 
shown in Fig. 33, thereby placing the long dimension 
of the drawing parallel to the long dimension of the 
rectangle, a much more satisfactory result is secured. 
It will, then, in all drawings, be necessary to find 
which is to be the longest dimension, and place this 
the long way of the sheet. 

INKING THE WORKING DRAWING 

It is well to divide the lines of a drawing into 
groups before starting the inking, that systematic 
and time saving work may be done. The primary 
lines of the drawing — object lines — may be placed 
in one group, the secondary lines in another group, 
and the free-hand work, which would include di- 
mensions, arrow-heads, and printing, in a third group. 
To distinguish the primary from the secondary lines, 
different colored inks are often employed. Blacky 
is always used for object lines, and red is often em- 
ployed for wdtness and dimension lines. Many times 
the black is used for both. In the latter case the 
distinguishing element is the character and size of 
the line. 

When inking drawings similar to those we have 
been studying, observe the following order: 



WORKING DRAWINGS 47 

ORDER FOR INKING 

Group 1. Object lines; heavy lines, with black ink. 
Horizontal lines; the upper ones first. 
Vertical lines; those at the left first. 
Oblique lines; the most convenient way. 

Group 2. Witness and dimension lines; light lines, 
with red ink. 
Horizontal lines; the upper ones first. 
Vertical lines; those at the left first. 
Oblique lines ; the most convenient way. 

Group 3. Arrow-heads, dimensions and printing; 
with black ink. 
Free-hand, with writing pen. Work 
from the upper left hand corner to 
the lower right. 

Group 4. Margin lines; heavy lines, with black ink. 
When these are made the same size as 
the object lines, they should be inked 
with Group 1. 



PLATE 3 

After laying off the margin and cut-off lines, divide 
the sheet into two equal rectangles by a vertical line 
through the center. Two problems are to be solved 
on this sheet, one at the left of the vertical line, and 
one at the right, to be taken, respectively, from the 
figures shown on pages 49 and 50. The problems 
will be selected by the instructor. 

Make three views, complete with dimension lines 
and dimensions. If possible, leave at least 1'' be- 
tween the views, and locate the drawing in the rec- 
tangle with equal spaces at the right and the left, also 
at the top and the bottom. Use Ught pencil lines. 

INKING 

Have the drawing complete in pencil before inking. 
When inking, follow the order given on page 47. 



WORKING DRAWINGS 



49 




Plates 



50 



MECHANICAL DRAWING 




Plate 3 



EXTRA PLATE 

Divide the rectangle made by the margin Hnes 
into two equal parts by a vertical line through the 
center. The problem to be drawn in the rectangle 
at the left will be selected from the upper part of 
page 52, that for the right-hand rectangle from the 
lower part of the same page. 

Make three views, complete with dimension lines 
and dimensions. If possible, leave at least 1'' be- 
tween the views and locate the drawing in the rec- 
tangle with equal spaces at the right and the left, also 
at the top and the bottom. Use light pencil lines. 

INKING 

Have the drawing complete in pencil before 
inking. When inking, follow the order given on 
page 47. 



52 



MECHANICAL DRAWING 




Plate 3. Extra Plate 



CHAPTER VII 

OBJECTS WITH OBLIQUE SURFACES 

PLATES 4, 5, AND 6 

In rectilinear objects, such as we have presented 
in Plate 3, the parallel lines of sight producing the 
views are at right angles to the surfaces drawn, 
thereby giving views which are exact reproductions 
of the surfaces them- 
selves. In Fig. 34, is ^ 
shown a wedged piece 
in which the front view, 
in case we selected the 
surface H, would be a 
triangle with base M N 
and altitude N S. The 
side view would be a rectangle with the horizontal di- 
mension equal to S 0, and the vertical dimension 
equal to N S, which is, of course, the same as the ver- 
tical dimension of the front view. The top view would 
have for its horizontal dimension the distance M N, 
the same as the horizontal dimension of the front 
view. (See Rule 2, page 35.) For the vertical di- 
mension of the top view we must use the distance 
S 0, which is the same as the horizontal dimension 




^"'9. O^ 



54 



MECHANICAL DRAWING 



of the side view. (See Rule 3, page 35.) These 
three views are shown in Fig. 35. 

The top view does not show the exact size of the 





o 
















s 
s 


S O 




^^^ 








ft 




1 

g. 35 


N 





obhque surface of the wedge, that surface being fore- 
shortened due to the fact that the hues of sight pro- 
ducing this view are not at right angles to the surface. 
It is not possible, with the three views shown, to give 
the true shape of the oblique surface; but, knowing 
that it is a rectangle, we may get one side by taking 
the line S N, and the other side by using the lines S O. 



TRACING 



The original mechanical drawing made in the 
drafting room very seldom finds its way into the shop, 
the shop drawing being in the form of a blueprint. 



OBJECTS WITH OBLIQUE SURFACES 55 

The requirements of the blueprinting process demand 
that the drawing be made on some transparent 
material. The common practice is to make the 
original drawing upon heavy drawing paper, and then, 
usually before inking this drawing, make a tracing 
upon some thin, transparent material, either tracing- 
paper or tracing-cloth. From this tracing the blue- 
print may be made. The tracing is made in ink, 
following the lines beneath, and the order of pro- 
cedure is the same as employed when inking the 
original drawing. 



PLATE 4 

After laying off margin and cut-off lines, divide 
the sheet into two equal rectangles by a vertical line 
through the center. Two problems are to be solved 
on this sheet, one at the left of the vertical line and 
one at the right, to be taken, respectively, from 
figures shown on pages 57 and 58. The problems will 
be selected by the instructor. 

Make three views, complete with dimension lines 
and dimensions. If possible, leave at least \" be- 
tween the views, and locate the drawing in the rec- 
tangle with equal spaces at the right and the left, also 
at the top and the bottom. Use light pencil lines, 

INKING 

Have the drawing complete in pencil before inking. 
When inking, follow the order given on page 47. 



I 



OBJECTS WITH OBLIQUE SURFACES 57 




Plate 4 



58 



MECHANICAL DRAWING 




Plate 4 



EXTRA PLATE 

Divide the rectangle made by the margin Hnes 
into two equal parts by a vertical line through the 
centei. The problem to be drawn in the rectangle 
at the left will be selected from the upper part of 
page 60, that for the right-hand rectangle from the 
lower part of the same page. 

Make three views, complete with dimension lines 
and dimensions. If possible, leave at least 1'' be- 
tween the views and locate the drawing in the rec- 
tangle with equal spaces at the right and the left, 
also at the top and the bottom. Use light pencil 
lines. 

INKING 

Have the drawing complete in pencil before inking. 
When inking, follow the order given on page 47. 



60 



MECHANICAL DRAWING 




F/p. ^ 



^-^ — 





! 

1 


^'r 




4: 




•o 












_,■ 




Eig /5 



Plate 4. Extra Plate 



PLATE 5* 

Make three views — top, front, and right side — of 
one of the pieces shown in perspective on pages 62 
to 64. The problem will occupy the entire sheet. 
Leave from V to W between the views, and locate 
the drawing on the sheet with equal spaces at the 
right and the left, also at the top and the bottom. 

INKING 

Have the drawing complete in pencil before inking. 
When inking, follow the order given on page 47. 

*NoTE. Plate 6 is to be finished before Plate 5 is taken from the 
board. 



62 



MECHANICAL DRAWING 




Plate 5 



OBJECTS WITH OBLIQUE SURFACES 



63 




64 



MECHANICAL DRAWING 




Plate 5 



PLATE 6 

Make a tracing from Plate 5. When inking, 
follow the order for inking given on page 47, except 
the directions for the witness and dimension lines. 
On the tracing make the lines included in Group 2 
black and very fine. This will require that the 
primary and secondary lines be inked in separate 
groups, as when the colored ink is used; for the 
former will be heavy lines and the latter fine lines. 
As the width of the line is the only distinguishing 
characteristic, it will be necessary to have the differ- 
ence in width quite marked. 



i 



CHAPTER VIII 



ASSEMBLY DRAWINGS 



PLATE 7 



All of the drawings which we have made up to the 
present time have been of a single piece and are 
called detail drawings. When two or more pieces, 
made to fit together, are drawn as they would be 
when they are put together, we have an assembly 
or construction drawing. The principles involved 
in working out the views are the same as for the single 
piece, although more care is 
required in the selection of 
views, in order to show the 
construction clearly and at 
the same time to use as few 
dotted lines as possible. 
Dotted lines on a drawing 
are always confusing, and in 
many cases one combination 
of views will mean fewer 
dotted lines than another. 
A little time arid study will 
determine the best combina- 
tion. 

In Fig. 36 are shown two parts of a joint used in 
woodworking, in which the tenon. A, of one piece 



^:ilJ 




/vy. 36 



ASSEMBLY DRAWINGS 



67 



fits into the recess cut into the other piece at B. An 
assembly drawing of this same joint, using three 
views, is shown in Fig. 37. In reahty, two views will 
show the details of construction clearly. These two 























































rn 


7 ^7 







views, with the dimensions for making each part, 
are illustrated in Fig. 38. When dimensioning a 
drawing of this character, dimension each of the com- 
ponent parts independent of the other. In Fig. 38, 
the dimensions A, B, C, D, and E are complete for 
making the horizontal piece and should be put on 
before any attempt is made to dimension the vertical 



68 



MECHANICAL DRAWING 

























— X- 
















1 


>. 








f 

o 

f 




_^_j — 




















r 


-^ 


J 




h B — - 








r/g. 3 8 



piece. When placing the dimensions on the vertical 
piece^ it will be found that some of the dimensions 
used for the horizontal piece may also be used for 
the vertical. Thus the dimension D will serve not 
only as the width of the cut on the horizontal piece, 
but also for the tongue on the vertical piece ; and the 
dimension B will serve equally well for the width of 
either piece. This leaves simply the dimensions X 
and Y to be added, in order to complete the dimen- 
sioning of the vertical piece, although the full di- 
mensions would include X, Y, B, D, and E. 



PLATE 7 

Divide the rectangle made by the margin hnes 
into two rectangles by a vertical line through the 
center. In the rectangles on pages 70 to 73 are 
shown perspective drawings of parts of different 
woodworking joints. Make three views — top, front, 
and right side — of two of these problems. When 
making the drawings, show the constructions clearly, 
and choose the views showing the fewest dotted lines. 
Leave about V^ between the views, and locate the 
drawing in the center of the rectangle. 

INKING 

Have the drawing complete in pencil before inking. 
When inking, follow the order given on page 47. 



70 



MECHANICAL DRAWING 



H-/2-^ 




Mitre Joint 





— End Mortise 
anct 7e/7orf yJo/nf.- 




Plate 7 



ASSEMBLY DRAWINGS 



71 



"5lflO 



Blind Mor//3e a/7c/ 
Tenon Jo/nf. 



■ ll-^ 



^ 



Ho/e exfencfs 
/n^o p/ece /p inc/7es 




■Enc/ Lap Jo/nf 





Plate 7 



72 



MECHANICAL DRAWING 



"pr^rra 



^K4J 




Box Jo/nf. — '2 



•f^ 




- Door Joint '^N^Vt^^l 

,i -A 



K£ 



Drainer Jo/nt 





Jr^^ 



■Doi/'efa// La JO <Jo/n/. 



Plate 7 



ASSEMBLY DRAWINGS 



73 



Th/s £ide of /70/e fa /3Gr^ 
i'li^^ ' . ^o /// f a/per ec/ - 

3/c/g of p/n _s-4::d=-'-T*- 





Pin Joint. 



Tab/e Leg Jo/rrf. 







■Ooyefo// Mor//se sJoZ/yf. 




Dove fa// Drat^er Joint — 



vn 



Nco 



ity* 



^ 



I 



,¥ 









\ 


1 




5 

16 


■ 1 










[_2i-i 



Plate 7 



EXTRA PLATE 

On pages 75 and 76 are given detail drawings of 
parts of woodworking models. Make assembly 
drawing, showing the construction in full lines, if 
possible. One problem will occupy an entire sheet. 

INKING 

Have the drawing complete in pencil before inking. 
When inking, follow the order given on page 47. 



ASSEMBLY DRAWINGS 



75 



:::::c 





~T^T 


1 


-i^ ^^i? 




f^i 








TsT 


1 


1 








-/i- 



^ bi' 






r/-i 






Jcal 





1" 



Defer //s of 



-Haiync/?ec/ Mor//se a/7c/ 7^/7or7 o/fc*//?/- 



r:ni 













oj 




J 


— 2 


-i(\j 




^^ 







Oefai/s of Brcfce Jo/nt 



Plate 7. Extra Plate 



76 



MECHANICAL DRAWING 





^ i 


















r "^4- 










t 

CM 


' 


f 


' 


^ 

1 










— Two pieces //Ae fh/s 


.— 






^CQ 












r 

! 






p^ 












roico 




— ^ C/?^ pJece //Ae //b/Is — 


_ 




- Th/o p/eces //ke //7/s. — 


- 





















TTvo /D/'eces //Ae //?/3 



1^ 



7'^ 






TTvo p/'eces //Ae //7/\s. 



Orpe p/'ece //Ae //?/3. 

De/a//^s of 

-/?ec/ar7pc//c//- Sox.- — 



Plate 7. Extra Plate 



EXTRA PLATE 

On pages 78 and 79 are given the assembly draw- 
ings of some woodworking joints. Make the detail 
drawings. 

INKING 

Have the drawing complete in pencil before inking. 
When inking, follow the order given on page 47. 



78 



MECHANICAL DRAWING 



— 


'i- 


— 


^ 


■t 


•1- 















1 


/ 


t 

1 


1 
■ — 2 ■ 


CVI 



Brc7cec/ Mor/^/se and 7e/^or7 xJo/'nf 







^* 










\ 
















\* 
































^' 










bZ ^/ 


— ^ 








■/« 












t 


"X 


•■/- 












"!!* 


I 


^M II 1 


-to 












S 1 




-./^« 














Sc-ar^ ^o/r>/. 





Plate 7. Extra Plate 



ASSEMBLY DRAWINGS 



79 





-l-rtl ^ 








-»T ,1 






7^ *' 




-M-AA- 




-i- 




^ 


? 


-^2 






Dov 


eA3 


//_ 


Jo/n/: 



-a- 


-7 

^8^ 


& 









2 — 


zr -, 


(0 . 




1 


1 

fVJ 


-- 







Ha/f Dove /a// Lop <Jo/nt. 



Plate 7. Extra Plate 



CHAPTER IX 
USE OF INSTRUMENTS 

(Curved Work) 
PLATE 8 

The compasses — As before stated, the compasses 
are provided with pencil and pen attachments and a 
lengthening bar. The lengthening bar is inserted 
between the fixed leg of the instrument and either 
the pencil or pen attachment, when it is desired to 
draw an arc whose radius is greater than the capacity 
of the regular instrument. For circles of large 
radii, the knuckle joints in the legs of the instrument 
should be bent to bring both needle point and pencil 
or pen attachment at right angles to the paper. 
This is absolutely necessary when the pen attach- 
ment is used, in order that both nibs of the pen come 
in contact with the paper. 

The compasses should never be placed on the scale 
when setting for a radius; this will eventually make 
holes in the scale, thereby ruining its accuracy. 
Measure to the left from the center about which the 
circle is to be drawn a distance equal to the radius 
of the circle, and after locating the needle point ex- 
actly at the center set the pencil point to the mark 
through which the arc is to be drawn. Use only 
one hand when drawing a circle, grasping the in- 
strument by the handle where the two legs are jointed. 
Rotate the compasses from the left, up over the top, 



USE OF INSTRUMENTS 81 

down through the right and bottom to the starting 
point. Always rotate the compasses in this direction, 
beginning at the left. Go over the Une only once, 
making a hght, fine fine. An attempt to make a 
heavy line will probably result in spreading the legs 
of the instrument, thus increasing the radius. 

The dividers — While the dividers are used for 
transferring distances from one part of the drawing 
to another part, they should never be employed for 
transferring a measurement from the scale to the 
drawing. Measurements on the drawing should be 
made directly from the scale. The dividers are most 
useful for dividing a line into a given number of 
equal parts, when the scale cannot be employed for 
the purpose. When thus used they should be held 
by the handle at the top of the instrument and should 
be rotated first on one side of the line and then on 
the other. Should the first setting not divide the 
line equally, a second setting, and probably more, 
will be required. If the divider is provided mth a 
hair-spring adjustment, this will be found very use- 
ful for adding to or subtracting from the original 
setting. Do not push the points of the instrument 
through the paper until the exact setting has been 
obtained. 

The bow instruments — These instruments are used 
on small work for the same purposes as the large ones 
are employed for large work, the directions for their 
use being the same as those given for the large com- 
passes and dividers. The bow instruments should 
be employed for everything within their capacity. 



/5o/3(^ 



PLATE 8 

Follow the directions given on the following pages. 
Use extreme care when working out the figures. 
Follow the directions for the use of the compasses 
and dividers. 

INKING 

The margin lines are the only straight lines to be 
inked. These should be inked last. All the arcs, 
with the exception of the circle about the point B, 
are to be inked. When inking the arcs, begin with 
the largest. 



DIRECTIONS FOR MAKING PLATE 8 

Three inches below the upper margin hne, draw a 
light horizontal line connecting the left and right- 
hand margins. On this line and 2i'' from the left- 
hand margin, locate a point. Letter this poinc A. 
Locate a point, to be lettered B, 4i'' to the right 
of point A; and 4i'' to the right of B locate a point, 
which we will call X. Through the points A, B, 
and X draw vertical lines about b'^ long, extending 
equidistant above and below the horizontal line. 

Draw a horizontal line 2Y' above the lower mar- 
gin line, connecting the left and right hand margin 
lines. On this horizontal line and 2'' to the left of 
the right hand margin line, locate a point. This 
point we will call D. Beginning with point D and 
measuring to the left, locate four more points 2\" 
apart. Call these points E, F, G, and H. Through 
these points draw vertical lines about V long, pro- 
jecting equally above and below the horizontal line. 

With point A, on the upper horizontal line, as a 
center, draw a circle having a ^" diameter. Using 
the same center, draw a dotted circle of IV' radius. 
When drawing the dotted line, make the dashes of 
equal length and have them equally spaced. Dashes 
should not be more than \" long and the space 
between dashes should equal about \ the length 



84 MECHANICAL DRAWING 

of the dash. Again using the center A, draw a circle 
of 1'' radius. This circle is to be drawn a full line. 
Concentric with the three circles just drawn, make a 
dotted circle of 1'' diameter. 

With a 1'' radius, draw^ a circle about the point B. 
Using the 45° triangle, draw lines through the center 
of this circle, dividing the circumference into eight 
equal parts. Beginning at the point where the verti- 
cal line through the center cuts the upper part of the 
circle and passing around to the right, number these 
points from 1 to 8, consecutively. With point 1 
as a center, and with a radius equal to the distance 
from 1 to B, draw a semicircle to the right of the 
vertical line. Using point 2 as a center, with the 
same radius, draw an arc from a point where it would 
intersect the semicircle about point 1, to the right, 
until it strikes point B. Draw about point 3, to 
the right, with the same radius, an arc from the point 
of its intersection with the arc about point 2, until 
it reaches point B. Complete the figure, using, 
in succession, points 4, 5, 6, 7, and 8. After the arc 
about point 8 is drawn, it will be necessary to extend 
the arc drawn about point 1 in order to make this 
arc the same as the others. 

With X as a center, draw a circle having a diameter 
of 4''. Using the bow dividers, divide the horizontal 
diameter into six equal parts. Beginning at the left, 
at the point where the horizontal line cuts the arc, 
letter the points a, b, c, d, e, f, and g. Point d will 
coincide with X. With b as a center, and a radius 
equal to the distance from b to a, draw a semicircle : 



USE OF INSTRUMENTS 85 

above the horizontal line. This semicircle should 
touch the point c. With the same radius, draw a 
semicircle below the horizontal line, using f as a 
center. This semicircle should touch the points e 
and g. With c as a center, and a radius equal to a c, 
draw a semicircle above the horizontal line. This 
semicircle should touch the point e. Using the same 
radius, draw a semicircle below the horizontal line, 
with the point e as a center. This semicircle will 
touch g and c. 

With points D, F, and H, on the lower horizontal 
line as centers, with a radius of 1}^', draw semi- 
circles above the horizontal line. With E and G as 
centers, and the same radius, draw semicircles below 
the horizontal line. Again using points D, F, and 
H as centers, draw semicircles with a U^ radius above 
the horizontal line. Below the horizontal line draw 
semicircles about points E and G, using a f radius. 



k 

k 



EXTRA PLATE 

Draw a Ih" square in the center of the sheet, and 
work out one of the figures shown on page 87. The 
centers for the arcs are determined by drawing hori- 
zontal and vertical lines across the square from points 
equally spaced on the sides. 

INKING 

Only the heavy lines of the figures are to be inked.^ 
Ink the large arcs first. 



USE OF INSTRUMENTS 



87 




No. a. 




a\ 



S3 



BD 



M> 




No. 4. 



No. 5. No. & 

Plate 7. Extra Plate 




EXTRA PLATE 

Draw one of the figures shown on page 89. All 
the fines radiating from the centers C may be ob- 
tained by using the triangles on the T square, either 
singly or in combination. Work carefully and 
accurately. Do not put the dimensions on the 
drawing. 

INKING 

Ink only the heavy lines of the figure. Ink all the 
arcs first, and then the straight lines. 



USE OF INSTRUMENTS 



89 




Plate 7. Extra Plate 



CHAPTER X 

CYLINDRICAL WORK 
PLATES 9 AND 10 

Whenever a circular piece or circular hole is shown 
in a mechanical drawing, a line is used to indicate the 
location of the center of the piece or hole. This line 
is known as a center line, and is included in the group 
of secondary lines already referred to. It represents 
the axis of revolution of the piece and becomes the 
axis of symmetry in the drawing. In Fig. 39 are 
shown two views of a double lever. The main center 
line of these views is the horizontal line marked 
"primary center line." This is the center line of the. 
main cylinder about which the model is constructed, 
and also serves as a center line for the hole through 
this main cylinder. As the cylinder and hole are 
concentric, the one center line will answer for both. 

On the circle view of a cylinder or a cylindrical 
hole, two center lines, both passing through the center 
of the circle, are drawn. These two lines are usually 
at right angles to each other. Thus, in Fig. 39, the 
vertical center line is drawn at right angles to the 
other main center line. This vertical center line is 
also a primary center line of the drawing, and, had 
the top view been drawn, would have extended up 



CYLINDRICAL WORK 



91 




■Secor?c/<7ry Cerrfer /./nes 



L::r: 



Rr/mary 



Cer?fe/- //>7e 



Fig. 39 



92 MECHANICAL DRAWING 

through that view, connecting it with the front view, 
as the horizontal center Une connects the front and 
side views. 

The two small cylinders on the arms extending out 
from the main cylinder also require center lines. As 
these are not the main center lines about which the 
drawing is made, they do not connect the two views, 
although they have to be shown on both views. 
These may be called secondary center lines. The 
vertical center line serves not only as the main center 
line for that view, but also as one of the center lines 
of the small cylinders and the holes in these cylinders. 

Alternate long and short dashes may be used to 
distinguish the center line from the other secondary 
lines of the drawing, although, as with all of these 
lines, this characteristic is dependent upon the sys- 
tems used in the different drawing-rooms in which the 
drawings may be made. These lines should be inked 
with the other secondary lines, and should be the 
same width and color. 

When a series of holes equidistant from a given point 
are to be represented, a line, called a circular center 
line, is employed. As its name implies, it is a circle 
drawn about the point from which the holes are equi- 
distant, passing through the centers of the holes. 
The line X, Fig. 40, is a circular center line answering 
as one of the center lines of all the small holes repre- 
sented on the front view. The other center line for 
these holes is a portion of a radial line drawn through 
the center of the circle representing the hole. These 
lines should not be drawn to the center of the piece, 



CYLINDRICAL WORK 



93 



but should extend only through the circles for which 
they are the center lines. This is shown clearly in 
Fig. 40. Notice also on this figure the center lines for 
the small holes on the side view. 

The primary center lines should be the first pencil 
lines to be drawn, and should be so located that when 




the drawing is complete it will be in the center of the 
rectangle. x\fter drawing the center hues, the meas- 
urements should be made from these and the drawing 
built up about them. 

The introduction of the curved hnes of the object 
and the center lines necessitates a new order for 
inking the drawing. When inking drawings similar 



94 MECHANICAL DRAWING 

to those shown in Figs. 39 and 40, follow the order 
given below: 

ORDER FOR INKING 

Group 1. Object lines; heavy lines, with black ink. 
Arcs; begin with the largest. 
Horizontal lines; the upper ones first. 
Vertical lines; those at the left first. 
Oblique lines ; the most convenient way. 

Group 2. Witness, center, and dimension lines; 
light lines, with red ink. 
Arcs; begin with the largest. 
Horizontal lines; the upper ones first. 
Vertical lines; those at the left first. 
Oblique lines ; the most convenient way. 

Group 3. Arrow-heads, dimensions, and printing; 
with black ink. 
Free hand, with writing pen. Work 
from the upper left to the lower right. 

Group 4. Margin lines; heavy lines, with black ink. 
When these are made the same size 
as the object lines, they should be 
inked with Group 1. 



PLATE 9 

Divide the rectangle made by the margin Hnes 
into two equal rectangles by a vertical line through 
the center. In the left-hand rectangle draw two 
views of one of the objects shown in perspective on 
page 96, and in the right-hand rectangle draw two 
views of one of the models shown on page 97. 

Select the views having the fewest dotted lines, 
consistent with a clear representation. Locate the 
center lines to bring the drawing in the center of the 
rectangle. 

INKING 

Have the drawing complete in pencil before inking. 
When inking, follow the order given on page 94. 



96 



MECHANICAL DRAWING 




Plate 9 



CYLINDRICAL WORK 



97 




Plate 9 



EXTRA PLATE 



Make two views of one of the objects shown on 
page 99. 

Follow the general directions given for Plate 9. 



CYLINDRICAL WORK 



99 




'4--H 



h-/2-i 




Be// Cr-crryA- 



Plate 9. Extra Plate 



PLATE 10 

Copy the two views shown in one of the rectangles 
on pages 101 to 106, and work out the third view. 
The problem will occupy the entire sheet. Locate the 
center lines to bring the drawing in the center of the 
sheet. Print the name of the piece under the draw- 
ing, making the capitals t&" high and the small 
letters \" high. 

INKING 

When inking, follow the order given on page 94. 



CYLINDRICAL WORK 



101 



1 


- ~y 


1 1 
1 1 


1 


1 
1 


1 


• 


'^ — zh— 


/' 


% 


— 2i- 




V 


J 




_[^ 


1 

1 


r 

1 


1 


! 


1 


— i — \~/ 


— zi-^ 


* 2i -* 


1 


1 1 


1 1 


1 
(- 






Plate 10 



102 



MECHANICAL DRAWING 




Plate 10 



CYLINDRICAL WORK 



103 



1 ■ 




1 • 1 


-f-^h— !v 




a 


h-//-|-'^--i— /iH 




"i f f 



^ ! '^ 



Connecf/np /^ocf Sfrc7 p. - 




Plate 10 



104 



MECHANICAL DRAWING 




Plate 10 



CYLINDRICAL WORK 



105 




o^ 



■oioo 



J 



3 



■ Eccer7/^n'c. 






^i-i 



I'^A 



, __v 



4i 



^3 




RacA/'n^ G/oncf. 



Plate 10 



106 



MECHANICAL DRAWING 





1 




J2 — 


-'i-^ 








t 

i 




- ,V1 


rr 








" 




.|.4. 






..!_.-.. 


1 — 


lit 
'"1T"" 


4, 




1 


i 1 
----1 -j 








to 

1 

1 




^ 

J 







S>ec7r/r7 Q. 






! 


- 




/7 


^<5>\;\^ 1 


_ — 






t 




1 


(j 


D 


j ) 1 




i-i.. 


\\ 




b/ 


1 
r 

1 

1- 


■if- 
_j -- 


^" 


L 




/3(yse for l^/se . 



Plate 10 



EXTRA PLATE 

Copy the two views shown in one of the rectangles 
on pages 108 and 109, and work out the third view. 
The problem will occupy the entire sheet. Locate 
the center lines to bring the drawing in the center 
of the rectangle. Print the name of the piece below 
the drawing, making the capitals ye" high and the 
small letters V high. 

INKING 

When inking, follow the order given on page 94. 



108 



MECHANICAL DRAWING 




::.r 



\- '^A -< 



Tr/p/e Le\/er 




Plate 10. Extra Plate 



CYLINDRICAL WORK 



109 
















K— 


1 


f 




Base /s reef ar7- 

Qu/ar /n for/n. 


-1- 


-1- 


TT 


1 
1 


' 1 




•0 


1 

1 ' 


1 

1 


\ 








i 






-Ik- 




-■--1 

1 ^ 

1 


_L_ 


> 


1 


\-\—\°^ 




4j 




\ .5-V 






1 ft- \ 




1 


1 1 


; 


: .1, 




1 •c - 


1 


L 






















1 

\/^^J-: / ITS 


^a 










Ver 






yy- 







Plate 10. Extra Plate 



CHAPTER XI 

SCALED DRAWINGS 

PLATE 11 

Many times the object to be represented in the 
drawing is of such a size that it is impossible to draw 
it full size upon a sheet that may be conveniently 
handled in the shop. In cases of this kind, the draw- 
ing is made to a reduced scale, and is called a scaled 
drawing. A scaled drawing is one in which the length 
of all the lines of the drawing bears a definite ratio 
to the length of the corresponding lines of the object. 
Thus in a dramng made one-half size, each Hne of 
the drawing will be one-half the length of the cor- 
responding hne of the object. 

Our United States standard system of measure- 
ments requires that the denominator of the fraction 
used in our scale shall be some multiple of two. The 
draT\dngs, therefore, wdll have to be made |, i, i or 
i size. It will be readily seen that it would be 
practically impossible to measure most dimensions, if 
a two-thirds or one-sixth scale were employed. 
Drawings should always be made to the largest pos- 
sible scale. If it is possible to use three-fourths 
size without crowding, do not make the drawing one- 
half size. It is, of course, easier for the workman to 



\ 



SCALED DRAWINGS 111 

work from the full-sized drawing, and the smaller 
the scale the more difficulty there will be in reading. 
Full size dimensions should be placed on the drawing; 
not the measurements of the drawing, but the di- 
mensions to which the object is to be made. 

A statement giving the scale to which the drawing 
is made should be printed on each scaled drawing. 
There are two ways in which this may be expressed. 
The one commonly used on machine drawings is 
Scale, I Size, or Scale, i Size. Because of the small 
scales employed, the architect uses the following: 
Scale, 3'' = r, or | in. = lfL 



PLATE 11 

Copy the two views given in one of the rectangles 
on pages 113 to 116, and work out the third view. 
Make the drawing to the largest possible scale. 
Place the title and the scale to which the drawing is 
made below the drawing. 

INKING 

When inking, follow the order given on page 94. 



SCALED DRAWINGS 



113 







W\ 











^— 2 - 






1 

1 


^'. 


2 




i 


.t 

1 , 


i 




i 


\^ 


-I'u 


-^ ' 






1 



Angle P/afe 




PacA/r ? g G/cfnc/. 



Plate 11 



114 



MECHANICAL DRAWING 



















1 




'n% 






1 ' 

1 


-- 


1 








.1 






1 




^ZZ^J 






3 


^~> 




— 2.-^ 






± 




<0 

r 


. 


---r'" 










A 




■ P/vof Bear/na. 






V 






f 94- 


^1 













-34 



V- 



€ 



'ii 



33 






Lf 



_t-_i 






i- Si 



3^'l 



Sv^ivel Bean' I 



09^ 




± 



Plate 11 



SCALED DRAWINGS 



115 




Plate U 



116 



MECHANICAL DRAWING 




Be// Cran/< Lever 











7^ 


t^ 


1 Ml 

L 


3^ 


/ / 
/ 


vf 


— -) 


H 


1 
1 


r 


















, 








^^Z 




1 




i«)i<o 


1 




^ 


r 1 ^ 


Ba 


i-L-i^ '-, 


^.'-i- 


i]:% 


_L 1 ,: 


c-^ >C - * / 


1 /, .. — 


~ 













Plate 11 



EXTRA PLATE 

Copy the two views given in one of the rectangles 
on page 118, and work out the third view. Make 
the drawing to the largest possible scale. Place the 
title and the scale to which the drawing is made be- 
low the drawing. 

INKING 

When inking, follow the order given on page 94. 



118 



MECHANICAL DRAWING 




£.cce/ifr/c C/a^n js/n o 3eor//7 ir. 



i-Hr|H 



'iH 



/i-t- — 4^ 



^S^S) 




3e-crr-/>7Q for /^/ar?er Oenfer 



Plate U. Extra Plate 



CHAPTER XII 



SECTIONAL VIEWS 



PLATE 12 




In the problems which have been presented thus 
far in the course, emphasis has been placed upon ex- 
pression with full lines in preference to dotted ones. 
Dotted lines are confusing on any 
drawing, and should be avoided 
wherever possible. To eliminate 
the dotted lines caused by the 
three views we have already dis- 
cussed, a system by which the in- 
terior of the object may be shown 
in full lines is employed. Views 
of this character are known as sec- 
tional views, and are obtained by 
passing an imaginary cutting plane 
through the object and making a 
drawing of the portion of the ob- 
ject remaining after the part cut off by the cutting 
plane has been removed. 

A double flanged cylinder with a circular hole pass- 
ing through it is shown in Fig. 41. Let us imagine 
that this cyhnder is cut in halves by a vertical plane 




120 



MECHANICAL DRAWING 




■^9. 



^^2 



passing through the axis. After passing this cutting 
plane through the piece, and removing the front half 
of the cylinder, we would have what is represented 
in Fig. 42. Two views of the model 
shown in perspective in Fig. 41 are 
given in Fig. 43, while in Fig. 44 
are shown two views after the imag- 
inary cutting plane has been passed 
through the piece. It will be seen 
that the front view only is altered, 
the top view remaining the same. 
The model represented is a com- 
plete cylinder, and not a half cylin- 
der; therefore the complete top view 
is necessary. The front view, which 
really represents only one-half of the 
cylinder, is produced by the imaginary cutting plane, 
and not an actual cutting plane; hence the complete 
top view. 

A comparison of the full front view in Fig. 43 and 
the sectional front view in Fig. 44 brings out the fact 
that the hole through the piece is represented by 
dotted lines on the former and by full lines on the 
latter. Also note that portions of the horizontal 
lines representing the lower part of the upper flange 
and the upper part of the lower flange have been 
omitted on the sectional view. It is common prac- 
tice to omit the dotted lines, when the representation 
is complete by full lines, even though every line of the 
object is not shown on the drawing. Had the flanges 
been square, as shown in Fig. 45, it would have been 



SECTIONAL VIEWS 



121 












1 






1 


1 
1 




1 

1 






^^9- 


^3 






/^f'g, *^*f- 



best to draw these dotted lines, in order to show the 
corner on the front view. 

The obhque hnes drawn across portions of the 
sectional views are called section lines. These are 
drawn only where the material of the model is cut 
by the cutting plane. In Figs. 44 and 45, they are 
not drawn across the area representing the hole 
through the piece, but only across those portions of 
the model where the cutting plane has come in con- 



122 



MECHANICAL DRAWING 



tact with the material of which the model is made. 
The section Hne may be made at any angle and in 
either direction. The most common angle is 45°, 

and the direction is 
usually from the lower 
left to the upper right, 
probably because of 
its convenience. Sec- 
tion lines should not 
be drawn with pencil, 
nor should they be 
spaced with the in- 
struments or scale. 
They should be inked 
with black ink, with a 
line finer than the fin- 
est line of the draw- 
ing, and should be 
spaced with the eye, 
care being taken not 
to have the lines too 
close together. For 
average work, spaces 
should be about ^''. 
When two or more 
pieces are in contact 
and a sectional view is used, the section lines for the , 
several pieces should be drawn in opposite directions. 
Should these pieces be so placed that one of them 
is in contact with two or more, it will be necessary 
to change the angle of the lines as well as the direction. 




SECTIONAL VIEWS 



123 



I 




124 MECHANICAL DRAWING 

In Fig. 46, page 123, the inner piece or spindle is in 
contact not only with the bearing, but also with the 
yoke at the end of the piece. The section lines for 
the spindle are drawn at an angle of 30° with the 
horizontal, from the upper left to the lower right. 
For the bearing, the lines are drawn at an angle of 
30° from the lower left to the upper right. The 
lines for the yoke are at an angle of 45°, and, though 
drawn in the same direction as the lines of the spindle, 
the difference is shown by the change in angle. 

The introduction of the section lines causes an- 
other group to be added to those already classified 
for inking. In all of the work hereafter, use the order 
for inking given below. 

ORDER FOR INKING 

Group 1. Object hues; heavy lines, with black ink. 
Arcs; begin with the largest. 
Horizontal lines; the upper ones first. 
Vertical lines ; those at the left first. 
Oblique lines; the most convenient way. 

Group 2. Witness, center, and dimension lines; light 
lines, with red ink. 
Arcs ; begin with the largest. 
Horizontal lines; the upper ones first. 
Vertical lines; those at the left first. 
Oblique lines; the most convenient way. 

Group 3. Arrow-heads, dimensions, and printing ; with 
black ink. 
Free hand, with writing pen. Work from 
the upper left to the lower right. 



SECTIONAL VIEWS 125 

Group 4. Section lines; very light, black lines. 

Finer than any other line of the drawing. 

Group 5. Margin lines; heavy lines, with black ink. 
When these are made the same size 
as the object lines, they should be inked 
with Group 1. 



PLATE 12 

Copy the two views shown in one of the rectangles 
on pages 127 to 131. Make one of the views a sec- 
tional view. 

INKING 

When inking, follow the order given on page 124. 
Use this order on all of your future work. 



SECTIONAL VIEWS 



127 








- 




1- 1 








«- 


/ 


1 1 








|-'i-| 








~?-"-rir 




? ^ 







- 


L. 




^i 



Piston 



Plate 12 



128 



MECHANICAL DRAWING 




F/anQecf Cou/o//'r p. 



[-H 



i 



-i ! 



_ J.. 



T 



r 00 




If 



P/sfon Soc /y. 



Plate 12 



SECTIONAL VIEWS 



129 




Plate 12 



130 



MECHANICAL DRAWING 




Plate 12 



SECTIONAL VIEWS 



131 




-2k 



w 



|ro«o[v< 



00,50 



:=^ 






37i 
3 team En cf /ne Cy/mc/er Hecrc/. — 




Guide for S^/ve/ Hecrcf 



Plate 12 



EXTRA PLATE 

Copy the two views shown in one of the rectangles 
on pages 133 and 134. Make one of the views a 
sectional view. 

INKING 

When inking, follow the order given on page 124. 



SECTIONAL VIEWS 



133 




Governor ^u//e y. 




Plate 12. Extra Plate 



134 



MECHANICAL DRAWING 









i-- 



D/orr?e /-ers ( y/ \^e/7 . 

arc ot sc/ e^es /WaAe 

of croi^r? ,-f; mo/s fhcrr> 







Cone Po//e y 



,^£^ 



-tJ-L_:. 



_ t- -i 

i . _ i - .1 
I 



2i 




F/anQ<?cf Pu/Ze y 



Plate 12. Extra Plate 



CHAPTER XIII 

PARTIAL SECTIONS 

PLATE 13 

In order to show both the exterior and the interior 
in full lines in a single view, a half section, shown in 
Fig. 47, is often employed. This, it will be noted, 
is a drawing of the model shown in perspective in Fip*. 
41, and the front view is a combination of the front 
views given in Figs. 43 and 44, page 121, the right 
half being the same as the right part of the full view, 
while the left portion is the same as the left half of the 
sectional view. The cutting plane to produce this 
front view would pass along the horizontal center line 
of the top view to the center of the piece, then along 
the vertical center line to the front of the view. De- 
noting the path by letters, the cutting plane would 
pass along the line ABC. Thus it will be seen that 
the path of the cutting plane need not be a straight 
line, as was the case in Figs. 44 and 45. In Fig. 47 the 
place where the cutting plane ends is shown by a full 
object line, but it is often the practice to use simply 
the center line to limit this sectioned area. This 
method is shown in Fig. 48. In this view all of the 
dotted lines are omitted. 

Another instance of a cutting plane not being con- 



136 



MECHANICAL DRAWING 














i 


1 








P 

> 






i 


i 















m 








1 






1 





F/s^. ^7 



F/ff. ^G 



tinuous is shown in Fig. 49. In this example the 
cutting plane passes along the horizontal center line 
to the shaft upon which the disc is mounted, thence 
around the shaft to the horizontal center line again, 
and along this center to the outside of the piece. 
This leaves the spindle or shaft in full on the front 
view, which leads to the statement that soM, cylin- 
drical parts should never he shown in section. The full 
length of the shaft is not shown in the front view and 



PARTIAL SECTIONS 



137 




138 MECHANICAL DRAWING 

ends at top and bottom in what are termed broken 
sections. This figure also shows the breaking of the 
section fines for the dimension, when the dimension 
has to be placed in the sectioned area. Note that 
the breaking of the section lines brings into prom- 
inence the 5x6^' dimension on the front view. 

Arms of pulleys and hand-wheels, ribs on castings, 
etc., should be placed back of the cutting plane, 
when a sectional view is used. The application of 
this statement to the arms of a pulley is shown in 
Fig. 50. The line of the cutting plane to produce 
the sectional view would be along the vertical center 
line of the side view. This would make the arm of 
the pulley in section; but, in cases of this character, 
we draw the sectional view as though the plane passes 
through the rim and hub, leaving the arm as a full 
view. By this method one is able to distinguish, 
by a glance at the sectional view, the character of 
the connection between the hub and rim of a pulley. 
A pulley with a web connection between rim and hub 
is illustrated in Fig. 51, and a comparison of the two 
sectional views will show the way in which one may 
differentiate between the two designs. Had the 
sectional view of the arm pulley been made by passing 
the cutting plane through the arm, the resultant 
view would have been the same as the sectional view 
of the webbed pulley, with no opportunity to dis- 
tinguish between the two, except by reference to 
the other view. By placing the arm back of the plane 
of the section, we emphasize the character of the de- 
sign. 



PARTIAL SECTIONS 



139 




140 



MECHANICAL DRAWING 





^ig- ^^ 



Fig. 53 



The sectional view of the model shown in Fig. 52 
gives the impression of a conical piece, while in reality 
it is a cylindrical piece with supporting ribs and rec- 
tangular base. While it is possible to see the exact 
shape by the combination of the front and top views, 
yet no one view should give a wrong impression. If, 
instead of the views given in Fig. 52, we had used 
the views shown in Fig. 53, the sectional view would 
give the correct impression of the general shape of 
the object. This would, then, be the proper view 
to employ. It is obtained by placing the ribs back 



PARTIAL SECTIONS 



141 



of the plane of the section, as we did the arms of the 
pulley in a previous illustration. This drawing also 
shows the size of the fillet where the cylinder joins 
the base, something which was not shown at all in 
Fig. 52. 

From the drawing given in Fig. 50, it is impossible 
to tell the shape of the arm of the pulley. We can 




Fig. 54- 



get the width and thickness, but whether it is rec- 
tangular, flat on the sides with rounded corners, or 
elhptical in section, we do not know. The section 
drawn on the arm at the right of the center shows the 
fcross section to be an ellipse. Here the view is 
^shown at right angles to the cutting plane, a practice 
[quite common in cases of this character. Often the 



142 MECHANICAL DRAWING 

line of the cutting plane is given and the section drawn 
in another place. This is illustrated in Fig. 54. In 
this figure the lines A B and C D represent the lines 
of two cutting planes, and the figures below the draw- 
ing show the shapes of the sections. It is necessary 
to distinguish them by letters and notes, as shown in 
the figure. 



PLATE 13 

Copy the drawing given in one of the rectangles 
on pages 144 to 146, making the upper half of one of 
the views in section. 



144 



MECHANICAL DRAWING 




PARTIAL SECTIONS 



145 




#■ . 


^SH 




xd 








Secf/onA-B 






'Tf\ 








\ . 


) 














1-- A 

\ 1 


-T-.^ 


/ 


1 


1 ri^ 


-0 


/ 






^ 






- 


— 




I'-- 



Gear B/anA. 




Fr/cf/on Cone. 



Plate 13 



140 



MECHANICAL DRAWING 





4__I 



t 



i:-- 



r 



— /i-^- 



/°//o/ i/V/7ee/. 



Plate 13 



EXTRA PLATE 

Follow the directions given in one of the rectangles 
on pages 148 to 150. 



148 



MECHANICAL DRAWING 



v5ec//o/7 c-n 



Make s/c/e i^/epv />? sec f /or?. 



Eccenfr/c. 




o 3ecf/o/7a/ i^/ew. 






L. 



t-'i-^ 



8i 




C/7UCA. 



Plate 13. Extra Plate 



PARTIAL SECTIONS 



149 



K/gM^ cy sec f /on a/ y/e^/ 



% ^ 






l^ 



Z 






r 



^^ 



1 



-2i H 




■ ■3 p'fyc//e Crar7A /^cgc/. 



f« 2 








_^ I I 






Bronz0 



P/a/r? Sear/'ng' i^//h Sush/n qr. - 



Plate 13. Extra Plate 



150 



MECHANICAL DRAWING 




Plate 13. Extra Plate 



APPENDIX 



CHAPTER XIV 

LETTERING 

CAPITALS 

Good lettering is an essential to good work in 
mechanical drawing. Plain, simple^ well-propor- 
tioned, properly spaced lettering will improve the 
appearance of any drawing, no matter how beauti- 
fully it may be executed otherwise; and it is equally 
true that the appearance of the drawing will be ruined 
by poor lettering. 

On almost all mechanical drawings, the Gothic 
type, an example of which is shown on page 154, is 
employed. Sometimes all capitals are used, but in 
the majority of cases the capitals and small letters 
will be found. When all capitals are used, the capi- 
tahzed letters are made higher than the others. 
(See Fig. 55.) A careful examination of the alphabet 
will show that the letters are composed of either 
straight lines, ellipses, or combinations of the two. 
For instance, the capitals H, N, M and others are 
composed entirely of straight lines ; the and Q are 
elHpses; C and G are portions of ellipses; while 
D, P, R, and others, are combinations of parts of 
ellipses and straight lines. Combinations of a similar 
nature will be found in the small letters. 



154 MECHANICAL DRAWING 



\BCDErQHIJKL 



MNOPQRSTU 



VWXYZ 



abcdefghijklmno 
pq rsfuvwxyz 



1234567890 



4i 2i 7| 



LETTERING 155 

The main body of the small letter should be two- 
thirds the height of the capital. A good size for 
practice work, in fact, for most lettering on a drawing, 
is 1^ of an inch for capitals and i of an inch for the 
main part of the small letter. Lines should always 
be drawn regulating the height, and the letters should 
exactly fill the space between the lines. 

Particular care should be used to make the slant of 
the letters uniform. This slant may be made any- 
thing between 60° and 75° with the horizontal, the 
latter being the better angle. In . 
the capitals A, V, X, and W, and \l/Af\JI j \^ 
the small letters v, x, and w, the '^'s^^ 

angle of the component parts may / / I'j H 
be determined by the use of a center / njss^ 
line. In the word '^Vanity," Fig. 55, 
the general slant is shown by the letters I, N, and T, 
and the slope of the parts of the letters V, A, and Y 
is obtained by laying off equal spaces each side of 
center lines drawn parallel to the letter I. 

The manner of obtaining the slant of the curved 
letters may best be illustrated by using O as an ex- 
ample. Draw a parallelogram (see Fig. 56) in 
which the upper and lower lines shall limit the height 
of the letters, and the right and left-hand lines shall 
represent the slant. Divide each side into two equal 
parts. This gives the tangent points of an elhpse 
to be drawn within the parallelogram. 

It should be perfectly understood that all of this 
work, with the exception of the lines to regulate the 
height of the letter, should be executed free hand, 



156 MECHANICAL DRAWING 

and that as soon as the student can trust himself, 
all of the construction for the curved letters should 
be omitted. When inking, only a small amount of 
ink should be used on the pen, and great care should 
be exercised not to spread the points. Avoid all 
shading and shade line effects. 

No definite rule can be given for the space between 
letters, this space varying with different combinations. 
The space between words should be about three times 
the average space between letters. 

SUGGESTED EXERCISES FOR HOME WORK 

Capital Letters 

(Make the capital letters jV" high) 

A series of par- 

1. I I I I I l~~ ^^^^ oblique hues 

about 1^'' apart. 
A series the same 
_____^_________________ as No. 1, with the 

2. I I I I I T~ addition of the 

horizontal line to 
form the letter L. 

The same as No. 
1, with the addi- 
tional line to make 
the letter T. 

A series of par- 
allel lines having 
alternate small and 
large spaces. 



3. ////// 



4. // // // // 



LETTERING 157 

Make the small spaces about A" and the large 

ones about A " - 

A series similar 
to No. 4, with the 
addition of the 
_^ cross line in the 

5. /— / /"T /~7 \~~i small spaces to 

form the letter H. 
Notice that the 
cross bar is slightly 
above the center. 

The same as No. 
4, with the addi- 
tional hne to make 
the letter N. 

The same as No. 
1, with additions 
to form the letter 
E. Note that the 

y —r rr — ~~r. r — upper horizontal 

line is shorter than 
the lower one, and 
that the middle 
one is slightly 
above the center. 

The same as No. 
1, with additions 

^ I l_ l_ l_ to form the letter 

^' i~ r r r ^ This is the let- 

ter E with the le wer 
line omitted. 



H 


H 


H 


H 




N 


N 


N 


N 




t- 


h 


h 


h 




t- 


h 


h 


h 



158 



MECHANICAL DRAWING 



9. 



K K hC-R 



10. 1^ M M M 



11 



A A A 'T^ 



12. 



Y \y V V 



13. ^ ^ w w 



The same as No. 
1, with the hnes to 
form the letter K. 

The width of the 
M is equal to the 
height. Either 
form may be used, 
although the one 
at the right is pre- 
ferable. 

First draw a ser- 
ies of center hnes 
about T&" apart. 
About these center 
lines construct the 
letters. After be- 
coming familiar 
with the relation of 
the component 
parts, draw a ser- 
ies without the use 
of the center lines. 

Follow the gen- 
eral directions 
given for No. 11. 

The center lines 
of the two parts of 
the W should be 
about \" apart. 
Having drawn the 
center hnes, con- 



LETTERING 159 

struct the letter. Finally, draw the letters without 

the center lines. 

Draw a series of 
center Unes as di- 
rected for No. 11. 
The intersection of 
the cross lines 
should be slightly 
above the center of 
the letter. 

The center hne 
of the letter forms 
the lower part of 



i^. X i X X 



15. Y Y Y Y~ the letter Y. The 

vertex of the V is 
slightly below the 
center of the letter. 
Draw the con- 
struction lines as 
directed for No. 4. 
, Form the letter by 



16. / Y / Yl ^^® ^^^ ^^ these 

Hues. Finally draw 
the letter without 
the use of the con- 
structions. 
Draw the con- 
. , ' struction lines to 

117- fjj [J [J [j the directions given 

for No. 4. Read 
the text given in 



160 MECHANICAL DRAWING 

connection with Fig. 56, page 155. Follow the di- 
rections there given. Finally, make the letter with- 
out the use of the construction lines. 

The same con- 
structions are used 
as for the letter 0. 
The C is the letter 
18 ~fi^ ~n 'M T^ O with a portion 

* -^ ^^—^ ^^ at the right left 

out. The G is the 
letter C with the 
additions shown. 

The combination 
of the lower part 
of the letter O with 

19. UJ U U U~ straight linesforms 
"'^^ the letter U. Use 

the same construc- 
tions as for the let- 
ter O, No. 17. 

The right hand 
portion of the let- 
ter D is the same 
as the correspond- 
ing part of the let- 
ter O. 
Note that the 
, / , , loop of the letter 

21. H h" H Af "" P is less than one- 
half of the height 
of the letter. The 



20- /) /; /; // 



LETTERING 161 

curve is one-half of an O, joining horizontal lines. 

The R is the letter P with an additional line. Use 

spacing given for No. 1. 

Note in the letter 

B that the upper 

loop is smaller than 

the lower one. 

I This letter is com- 

22. j^ J-j ^ ^ " posed of curves 
' similar to the letter 

O, joined to hori- 
zontal lines. Use 
the spacing given 
for No. 1. 

The letter S, 
probably the most 
difficult of all the 
letters to make, is 
one continuous 
curve. Consider- 
able practice will 
be required to 
make this letter 
well. Use the 
spacing given for 
No. 4. 

SMALL LETTERS 

Some of the small letters are exactly the same shape 
and have the same proportions as the capitals, the 
only way of distinguishing them from the capitals 



23- H S S S 



162 MECHANICAL DRAWING 

being by the height. A reference to page 154 will 
show that this is true of the letters c, o, s. v, w, x, and 
z. The letter 1 is a straight line, resembling the 
capital I. The main lines of the t and i are also 
straight lines. The small u is similar to the capital 
U, only the straight line at the right continues down 
below the loop. The letters f, j, k, and r are easily 
formed, and require no special directions. The 
letters a, b, d, g, p, and q are based upon the letter 
o and a straight line tangent. The upper parts of 
the loops of the h, m, and n is the curve of the upper 
part of the letter o. From this it will be seen that a 
perfect mastery of the curves of the letter o is ab- 
solutely necessary. 

SUGGESTED EXERCISES FOR HOME WORK 

Small Letters 

(Make the body of the small letters |" high) 

The letter o until 
perfectly mastered . 
Make the let- 



24. O O O n — ~ ^^^^ ^'^ ^^^ have 

a space of about A'' 
between each 
letter. 

The letter o with 
the tangent 
straight line form- 



25. CJ CJ n 0~~ ing the letter a. 

Many think it bet- 
ter to draw the 
straight line first. 



1 



26- ^ b b ( T ^ S. 



LETTERING 163 



The letters b and 
d consist of the let- 
ter o with the 
straight line tan- 
gent. Notice that 
the d is shorter 
than the b. 

The letter o with 
the straight line 
tangents extending 
below the line 



r>y — ^ j^ 1^ Y^ — forms the p and q. 

'^ ' - H H — H W - Notice the sHght 

curve at the lower 
part of the straight 
line of the q. 

The small e is 
the letter c with 
— the horizontal line 



— ^ C! S ^ — addition. It is 

best to draw the 
horizontal line 
last. 

The loops of the 
h and n are the 

— ^ ^^^i -^ ^ same as the upper 

29. ZT] — rr n f) p^^^ ^f ^^^ ^^^^^^ 

o. The remaining 
parts of the letters 
are made up of 
straight lines. 



164 MECHANICAL DRAWING 

The m is similar 

30. m m rrr ^ ^^ ^^^ ^^ ^"^^ ^^^ 

loops are nar- 
rower. 

FIGURES 

Copy the series of figures given on page 154, until 
a perfect mastery has been obtained. 



CHAPTER XV 
GEOMETRICAL DEFINITIONS 



POINT 

A point indicates position only, and has no dimen- 
sion. 

LINES 

A line is produced by the motion of a point and has 
dimension in length only. (In drawing a line with 
a pencil, the successive positions of the pencil point 
produce the line.) 

Lines may be straight, curved, broken or mixed. 

A straight line is a line 
which has the same di- 
rection throughout its en- 
tire length. See Fig. 57. 
quently called a right line. 

A curved line is a line no 
part of which is straight. 
See Fig. 58. 

A broken line is a ser- 
ies of straight lines drawn 
in different directions. 
See Fig. 59. Fig 



Fig. 57 



A straight line is fre- 




166 



MECHANICAL DRAWING 




Fig. 60 




A mixed line is a line composed of straight and 

curved lines. See Fig. 60. 
Straight lines are often 
called simply lines; and 
curved lines, curves. 
Straight lines may be horizontal, vertical or oblique. 
A line drawn from left to right is termed a hori- 
zontal line. A horizontal 
line is shown at A B, 
Fig. 61. 

Lines drawn in the op- 
posite direction are called 
vertical lines. Line C, 
Fig. 61, is a vertical line. 
Any straight line neither horizontal nor vertical 
is called an oblique line. See lines D 0, Fig. 61. 
Parallel lines are everyw^here equally distant from 

each other. The lines 

shown in Fig. 62, are 

Fig. 62 parallel. 

A line is perpendicular to another line when it 
meets that line so as not to incline towards it on either 
\ ^ side. (When speaking of 

perpendicular lines, the 
relation of one line to 
another is always under- 
stood. Thus, a vertical 
line when alone is not a 
^^^" ^^ perpendicular and is only 

spoken of as such when it is referred to in connection 
with a horizontal line. The horizontal and vertical 



GEOMETRICAL DEFINITIONS 



167 



lines in Fig. 61 are perpendicular, which is equally 
true of the two lines shown in Fig. 63.) 



ANGLES 



The opening between two straight lines which 
meet is called an angle. The lines M R and M N, 
Fig. 64, form an angle. ^ 

The lines are called the 
sides of the angle, and 
the point of meeting is 
known as the vertex. 

The size of an angle ^ 

depends, not upon the 

length of its sides, but upon the amount of the open- 
ing between the sides. 

When the sides of an angle are drawn in opposite 
directions they form a 



straight angle. Lines 


A 




drawn in opposite di- ^^^- ^^ 




rections from the point 


A 




A, Fig. 65, form a 






straight angle. 






A right angle is formed 






when the sides are per- ^ 


S 


C 


pendicular. The angles ^ 


^IG. 66 




A B C and A B D, Fig. 




^^^ 


66, are right angles. 






Every angle less than ^^„^ 


^^^^^ \ 




a right angle is an acute ^^-^""^^ 






angle. See Fig. 67. i 


^iG. 67 





168 



MECHANICAL DRAWING 




Fig. 68 



When an angle is greater than a right angle and 

less than a straight angle, 
the a n g l«e formed is 
called an obtuse angle. 
See Fig. 68. 

An angle greater than 
a straight angle and less 
than two straight angles 
is called a reflex angle. 
Fig. 69 represents a re- 
flex angle. 

Two angles are com- 
plementary when their 
sum is equal to a right 
angle. Each is called 
the complement of the 
other. In Fig. 70, the 
angles L N and M O 
N are complementary. 

When the sum of two 
angles is equal to a 
straight angle, the angles 
are called supplementary, 
and each is called the 
supplement of the other. The angles W X Y and 
W X Z, Fig. 71, are supplementary. 




TRIANGLES 



A triangle is a plane surface bounded by three 
straight lines. The bounding lines are called the 
sides of the triangle, the angles formed by the sides 



GEOMETRICAL DEFINITIONS 



169 




Fig. 72 



are called the angles of the triangle and the vertices 
of these angles are the vertices of the triangle. The 
base of a triangle is the 
side upon which it is sup- 
posed to stand. The 
angle opposite the base 
is known as the vertical 
angle, and the vertex of 
this angle is called the 
vertex of the triangle. 

The altitude of a tri- 
angle is the perpendicu- 
lar distance from the 
vertex to the base or the 
base produced. See line 
A B, Figs. 72 and 73. 




Fig. 73 



Triangles classified hy sides 

An equilateral triangle is one having all of its sides 
equal in length. See 
Fig. 74. This triangle 
is frequently called equi- 
angular, as all of its 
angles are also equal. 

An isosceles triangle is 
one having two of its 
sides equal. See Fig. 75. 
Two of the angles of an 
isosceles triangle are also 
equal. 

A scalene triangle is one having no two of its sides 




Fig. 74 



170 



MECHANICAL DRAWING 




Fig. 75 



Fig. 76 



equal. See Fig. 76. None of the angles of a scalene 
triangle are equal. 

Triangles classified by their angles 



A right-angled triangle 
or right triangle is one 
having a right angle. 
See Fig. 77. 




Fig. 77 




An acute-angled tri- 
angle is one having three 
acute angles. See Fig. 78. 



Fig. 78 




An obtuse-angled tri- 
angle is one having an 
obtuse angle. See Fig. 79. 



Fig. 79 



GEOMETRICAL DEFINITIONS 



171 



QUADRILATEKAL 



A quadrilateral is a 
plane surface bounded by 
four straight lines. 

A trapezium is a quad- 
rilateral which has no two 
of its sides parallel. See 
Fig. 80. 

A trapezoid is a quadri- 
lateral having two and 
only two of its sides par- 
allel. See Fig. 81. 

A parallelogram is a 
quadrilateral having its 
opposite sides parallel. 
There are four kinds of 
parallelograms: the rec- 
tangle, the square, the rhomboid, 
and the rhombus. 

A rectangle is a parallelogram 
whose angles are all right angles. 
Rectangles are shown in Figs. 82 
and 83. 

A square is a rectangle all of 
whose sides are equal. See Fig. 83. 

A rhomboid is a par- 
allelogram whose angles 
are not right angles. 
Figs. 84 and 85 represent 
rhomboids. 




Fig. 82 



Fig. 83 




172 MECHANICAL DRAWING 




Fig. 85 



A rhombus is a rhom- 
boid all of whose sides 
are equal. See Fig. 85. 



POLYGONS 



A polygon is a plane surface bounded by straight 
lines. This term is usually applied to figures hav- 
ing more than four sides. The number of sides de- 
termines the name of the polygon. 

A polygon of five sides is called a pentagon; one of 
six sides is a hexagon, one of seven sides is a heptagon, 
one of eight sides is an octagon, one of nine sides is a 
nonagon, and one of ten sides is a decagon. 

A regular polygon has all of its sides and all of its 
angles equal. 

A polygon is irregular when either sides or angles 
are unequal. 

CIRCLE 

A circle is a plane figure 
bounded by a curved line called 
the circumference, every point 
of which is equidistant from 
a point within called the center. 
See Fig. 86. 

The radius of a circle is a 
straight line drawn from the 
center to a point in the cir- ^^^- ^^ 




GEOMETRICAL DEFINITIONS 



173 




Fig. 87 



The arc 



cumference. Line A B, Fig. 87, is a radius. All 
the radii of a circle are equal. 

The diameter of a circle is a straight line drawn 
through the center and 
joining two points in the 
circumference. Line C 
Dj Fig. 87, is a diameter. 
A diameter is equal to 
two radii. 

i| An arc of a circle is any 
'part of its circumference, 
as E K H, Fig. 87. An 
, arc equal to one-half of the 
i circumference is called a semicir cumference. 
' C K D, Fig. 87, is a semicir cumference. 

A chord is a straight hne joining the extremities 
> of an arc. See hne E H, Fig. 87. 

A tangent is a straight 
line which touches the cir- 
cumference of a circle but 
does not intersect it, as 
M N, Fig. 87. The point 
at which the tangent 
touches the circle is called 
the point of tangency. 
The tangent is always 
perpendicular to the ra- 
dius at the point of tan- 
gency. 
A segment of a circle is the area bounded by an arc 
cand its chord. See Fig. 88. A segment equal to 




Fig. 88 



174 



MECHANICAL DRAWING 



one-half the circle is called a semicircle. See R V T O, 
Fig. 88. 

A sector is the area bounded by two radii and the 
arc which they meet. See Fig. 88. When the radii 
are perpendicular, the sector equals one-fourth of 
a circle and is called a quadrant. See R Y, Fig. 88. 

Every circle is supposed to be divided into 360 
parts^ called degrees, which are used as a measurement 
for angles. An arc of a semicircle^ or straight angle, 
is equal to 180 degrees. An arc of a quadrant, or 
right angle, is equal to 90 degrees. 

SOLIDS 

A polyhedron is a solid bounded by planes. The 
bounding planes are the faces, and their intersections 
are the edges of the polyhedron. 

Polyhedrons are classified according to the shape 
and relation of their faces. 

Prisms 

A prism is a polyhedron 
of which two opposite par- 
allel faces, called bases, are 
equal and parallel poly- 
gons, and the other faces, 
called lateral faces, are par- 
allelograms. See Figs. 89 
and 90. The intersections 
of the lateral faces of a 
prism are called lateral 
edges. 
The altitude of a prism is the perpendicular dis- 
tance between the bases. 



Fig. 89 



GEOMETRICAL DEFINITIONS 



175 



A right prism is one whose lateral edges are per- 
pendicular to the bases. See Fig. 89. 

A regular prism is a 
right prism whose bases 
are regular polygons. 

An oblique prism is one 
whose lateral edges are 
not perpendicular to the 
bases. See Fig. 90. 

A truncated prism is the 
part remaining between 
the base and a cutting 




Fig. 90 




plane oblique to the base 
which intersects all of the 
lateral edges. A trun- 
cated prism is shown in 
Fig. 91. 

Prisms are named by 
their bases. They are 
triangular, square, rec- 
FiG. 9i. tangular, hexagonal, etc., 

as the bases are triangles, square, rectangles, hex- 
agons, etc. 

Pyramids 

A pyramid is a polyhedron one face of which, 
called the base, is a polygon and whose lateral faces 
are triangles whose vertices meet in a common point 
called the vertex of the pyramid. See Fig. 92. 

The altitude of a pyramid is the perpendicular dis- 
tance between the base and the vertex. 



176 



MECHANICAL DRAWING 




Fig. 92 



A regular pyramid is a 
pyramid whose base is a 
regular polygon the center 
of which is in a perpen- 
dicular to the base let fall 
from the vertex. 

A pyramid is triangu- 
lar, pentagonal, octogonal, 
etc., as its base is a tri- 
angle, a pentagon, an oc- 
tagon, etc. 
The frustrum of a pyramid is the portion remaining 
between the base and a 
cutting plane parallel to 
the base which cuts all of 
the lateral edges. See 
Fig. 93. 

The altitude of the frus- 
trum of a pyramid is the 
perpendicular distance between the base and the cut- 
ting plane parallel to the base. 

Cylinders 

A cylindrical surface is a 
curved surface generated 
by a moving straight line 
which constantly touches 
a given curve, and moves 
so that any two positions 
are parallel. See Fig. 94. 
In this figure, if the line 
A B moves parallel to the 




Fig. 93 




GEOMETRICAL DEFINITIONS 



177 



position lettered and is constrained to follow the 
curve A E H, a cylindrical 
surface is produced. Any 
position of this moving 
line, E F, parallel to A B, 
Fig. 94, is called an ele- 
ment of the surface. 

A cylinder is a solid 
bounded by a cylindrical 
surface and two parallel ^^^' ^^ 

planes, called bases. See Figs. 95 and 96. 

A right cylinder is one whose elements are per- 
pendicular to the bases. 
^""^ "^"^ See Figs. 95 and 96. 

When the elements 
of the cylindrical sur- 
face are not at right 
angles to the bases, the 
cylinder is called an ob- 
lique cylinder. 

A circular cylinder is 
a cylinder whose bases 
are circles. See Fig. 96. 
The altitude of a cylinder is the perpendicular dis- 
tance between the planes of its bases. 

Cones 



Fig. 96 



A conical surface is a curved surface generated by a 
moving straight line one point of which is fixed while 
the line is made to follow a given curve. In Fig. 97, 



178 



MECHANICAL DRAWING 



the line A B in its several positions passes through the 

fixed point A at the same 
time touching the curve 
BCD. 

Any position of the 
moving line is called an 
element of the conical 
surface. Lines A B, A C, 
and A D, Fig. 97, are ele- 
ments of the surface. 




Fig. 9- 




The fixed point through which the elements pass is 
called the vertex. 

A cone is a solid bounded 
by a conical surface and a 
plane surface cutting all the 
elements of the conical sur- 
face. See Fig. 98. 

The altitude of a cone is 
the perpendicular distance 
between the vertex and the 
plane of the base. ^^^- ^^ 

A circular cone is one whose base is a circle. 

A right circular cone is a 
circular cone whose vertex 
_ lies in a line drawn per- 
pendicular to the plane of 
the base from its center. 
The frustrum of a cone 
is the part contained be- 
tween the base and a cutting plane parallel to the 
base. See Fig. 99. 




GEOMETRICAL DEFINITIONS 179 

The altitude of a frustrum is the perpendicular 
distance between the base and the cutting plane 
parallel to the base. 

Sphere 

A sphere is a solid bounded by a curved surface 
every point of which is equidistant from a point 
within called the center. 

The radius of a sphere is the straight line drawn 
from the center to the bounding surface. All radii 
are equal. 

The diameter of a sphere is a straight line drawn 
through the center and terminating in the spherical 
surface. The diameter is equal to two radii. 



CHAPTER XVI 

GEOMETRICAL PROBLEMS 

In the figures accompanying these problems, the 
given Hnes are made heavy and full, the required 
lines are made heavy with a long and short dash, 
and the construction lines are made full, light lines. 



GEOMETRICAL PROBLEMS 



181 






PROBLEM 1 

To bisect a straight line 
— With the ends A and B 
as centers and a radius 
greater than one-half the 
length of the line, draw 
^ arcs C and D intersecting 
on each side of the line. A 
line drawn through these 
intersections will bisect and 
be perpendicular to the 
given line. 

PROBLEM 2 

To bisect an arc — Draw 

the chord of the arc and 
bisect this chord. This 
bisector will biseqt the arc 
and will pass through the 
center about which the 
arc is drawn. 

PROBLEM 3 

To draw a perpendicular 
to a line from a point near 
the center of the line — 
Using the given point A as 
a center, with any radius 
draw arcs 1 and 2, cutting 
the given line at B and C. 
With these points of inter- 
section as centers, draw the 



182 



MECHANICAL DRAWING 



arcs D and E. A line drawn from the point of in- 
tersection of these arcs to the point A will be per- 
pendicular to the given line. 

PROBLEM 4 

To draw a perpendicular to 
a line from a point at or near 
the end of the line — With 
any radius and the given 
point A as a center, draw 
arc intersecting the given 
line at B. With B as a center 
and the same radius, draw 
arc 2 cutting arc 1 at the 
point C. With C as a center 
and the same radius, draw 
arc 3, cutting arc 1 at D. 
With D as a center and the 
same radius, draw arc 4 cutting arc 3 at E. A line 
drawn from E to A will be perpendicular to the given 
line. 

PROBLEM 5 

To draw a perpendicular to a 
line from a point outside of 
and near the end of the line 

— Through the given point 
A draw any line, such as A 
B, intersecting the given 
line. Find the point C by 
bisecting the line A B. (See 
Problem 1.) Draw the semi- 





GEOMETRICAL PROBLEMS 



183 



circle A B D with C as a center. A line connecting 
A and D will be perpendicular to the given line. 



PROBLEM 6 




To draw a perpendicular to 
a line from a point outside of 
and near the center of the 
line — With the given point 
A as a center with any ra- 
dius, draw arc 1, intersect- 
ing the given line at B and 
C. With points B and C 
as centers and equal radii, 
draw arcs 2 and 3, inter- 
secting at D. The line A 
D is the required perpen- 
dicular. 



PROBLEM 7 




To draw a line through a 
given point parallel to a 
given line — With the given 
point A as a center with 
any radius, draw arc 1, in- 
tersecting the given line at 
B. With B as a center with 
the same radius, draw arc 
2 through A intefrsecting 
the given line at C. With 
a radius equal the distance 



184 



MECHANICAL DRAWING 



C A and B as a center, draw arc 3, intersecting arc 1 
at D. A line drawn through A and D will be par- 
allel to the given line. 




PROBLEM 8 

To divide a straight line into 
any number of equal parts — 

At any angle with the given 
line, A B, draw an indefinite 
line A C. Lay off on this 
line the required number of 
equal spaces. Through the 
points thus obtained draw 
a series of lines parallel to 
a line connecting the last 
point and the end of the line 
to be divided. (See Prob- 
lem 7.) In the accompany- 
ing figure, the line A B is 
to be divided into five equal 
parts. On A C five equal 
spaces are laid off. Lines 
drawn through points 1, 2, 
3, and 4 parallel to a line 
connecting B and 5 will 
divide the line A B into 
five equal parts. 



PROBLEM 9 

Upon a straight line to construct an angle equal to a 



GEOMETRICAL PROBLEMS 



185 




given angle — Let A B C be 
the given angle and D E 
the given line. With B as 
center and anyradius, draw 
arc 1, cutting the side of the 
angle at F and G. With D 
as a center and with the 
same radius, draw arc 2, 
cutting D E at H. With 
F as a center, draw arc 3 
through G. With the same 
"c" radius and with H as a 
center, draw arc 4 cutting 
arc 2 at K. Angle K D H 
will equal angle ABC. 



PROBLEM 10 




To bisect an angle — With 
A as a center and any 
radius, draw an arc, inter- 
secting the sides of the 
angle at B and C. With 
B and C as centers and 
equal radii, draw arcs, in- 
tersecting at D. Line D 
A will bisect the angl'e 
B A C. 



186 



MECHANICAL DRAWING 



PROBLEM 11 




To construct an equilateral 
triangle on a given base, — 
The line A B is the given 
base. With A as a center, 
draw arc 1 through B. 
With B as a center, draw 
arc 2 through A and inter- 
secting arc 1 at C. Lines 
C A and C B complete the 
triangle. 



PROBLEM 12 




To construct an isosceles 
triangle on a given base, 
having given the length of the 
equal sides — The line A B is 
the given base and C D is 
the length of the equal 
sides. With the ends of 
the line A B as centers and 
a radius equal to the length 
of the line C D, draw arcs 
intersecting at E. The 
lines A E and B E com- 
plete the required isosceles 
triangle. 



GEOMETRICAL PROBLEMS 



187 



PROBLEM 13 



To construct a scalene 
triangle, the length of the 
sides being given — Let A 
B, C D, and E F be the 
length of the sides. With 
A as a center and the 
length of the side C D as 
a radius, draw arc 1. 
With B as a center and 
a radius equal to the 
length of the side E F, 
draw arc 2, intersecting 
arc 1 at H. Lines H A 
and H B complete the re- 
quired scalene triangle. 



PROBLEM 14 




To construct a square, 
the length of the sides be- 
ing given — The line A B 
is the length of one side 
of the square. Erect a 
perpendicular to A B at 
the point B. (Problem 
4.) With B as a center, 
draw an arc through A, 
cutting line B C at C. 
With A and C as centers 
and the same radius, 



188 



MECHANICAL DRAWING 



draw arcs 4 and 2 intersecting at D. 
and C D complete the required square. 



Lines A D 




PROBLEM 15 

To circumscribe a circle 
about a triangle — Bisect two 
of the sides of the triangle, 
as A B and B C. (Problem 
1.) With the intersection 
of these bisectors, point D, 
as a center, draw an arc 
through point A. This 
will be an arc of a circle 
passing through A, B, and C. 

B PROBLEM 16 

To circumscribe a circle 
about a square — Draw the di- 
agonals A C and B D inter- 
secting at E. With E as a 
center and radius E B, draw 
the circumscribing circle. 

PROBLEM 17 

To inscribe a circle within 
a triangle — Bisect two of 
the angles. (Problem 10.) 
Through D, the intersec- 
tion of these bisectors, 
draw D E perpendicular to 
A C. (Problem 6.) With 
D as a center and radius 
D E, draw the required 
inscribed circle. 



GEOMETRICAL PROBLEMS 



189 



PROBLEM 18 




To draw a tangent to a 
circle at a given point on the 
circumference — T h r o u g h 
the given point A, draw 
the radial line A C. Erect 
a perpendicular to A C at 
the point A. (Problem 4.) 
The perpendicular A B is 
the required tangent at A, 
and the point A is the point 
of tangency. 



PROBLEM 19 




To draw a tangent to an 
arc at a point on the arc, 
when the center is not 
known — With the given 
point A as a center, draw 
arcs 1 and 2, cutting the 
arc at B and C. Draw 
the chord B C. Through 
the point A draw a line 
parallel to B C. (Prob- 
lem 7.) This line will be 
tangent to the arc at the 
point A. 



PROBLEM 20 

To draw a tangent to a circle from a point outside the 



190 



MECHANICAL DRAWING 





circle — From the given point 
A draw a line to the center 
of the circle. Find point 
B by bisecting the line A C. 
(Problem 1.) With B as 
a center and radius B A, 
draw semicircle 1, intersect- 
ing the circle at D. The 
line DA will be tangent to 
the circle at D. 



Note. — If from any point on 
the arc of a semicircle lines be 
drawn to the ends of the diameter, 
the included angle will be a right 
angle. In the figure, the angles 
A C B, A D B and A E B are right 
angles. 



PROBLEI^ 21 

To draw an arc of a given 
radius tangent to two con- 
verging lines— Let A B and 
C D be the converging lines 
and E F the given radius. 
At any points, I and J, draw 
perpendiculars to A B 
and C D. (Problem 4.) 
Make I G and J H equal to 
E F. Draw H K and G L 



GEOMETRICAL PROBLEMS 



191 



parallel to the lines C D and A B. (Problem 7.) 
From M draw M S and M T perpendicular to A B 
and C D. (Problem 6.) With M as a center and 
radius M T, draw the required arc tangent to the 
converging lines at S and T. 



PROBLEM 22 




To draw an arc of a given 
radius tangent to two circles 
of fixed diameters — Let C 
D be the given radius. 
From A and B, the centers 
of the given circles, draw 
any indefinite lines A K 
and B L. Make G K and 
H L equal to C D. With 
B as a center and radius 
B L, draw arc 1. With 
A as a center and radius 
A K, draw arc 2 intersect- 
ing arc 1 at M. M is the 
center of the required tan- 
gent arc. Lines M A and 
M B will determine points 
of tangency T and S. 



PROBLEM 23 

To draw an arc of a given radius tangent to a given 
line and arc — Let A B be the given radius, C D the 
given line and E H S the given arc. Draw any radial 



192 



MECHANICAL DRAWING 




line G H. Measure off H K 
equal to A B. With G as a 
center and radius G K, draw 
arc 1. Draw line L M par- 
allel to and a distance equal 
to A B from C D. (Prob- 
lems 7 and 21.) Where LM 
cuts arc 1, draw N T per- 
pendicular to C D. (Prob- 
lem 6.) With N as a center 
and radius N T^ draw the re- 
quired tangent arc. T is 
one point of tangency^ and 
the other one may be ob- 
tained by extending G N 
to S. 



PROBLEM 24 




To construct an angle of 6o 
degrees — Let A B be one 
of the sides. With A as a 
center and any radius, draw 
arc 1, cutting A B at C. 
With C as a center and 
the same radius, draw arc 
2 cutting arc 1 at D. Line 
iS A D will make an angle of 
60 degrees with A B. 



GEOMETRICAL PROBLEMS 



193 





PROBLEM 25 

To construct an angle of 
30 degrees — The line A B 
is one of the sides. With 
any point X as a center 
and radius X A, draw a 
semicircle cutting the line 
A B at C. With C as a 
center and the same radius, 
draw arc 2 cutting arc 1 
at D. AD will make an 
angle of 30 degrees with 
AB. 

PROBLEM 26 

To draw a hexagon, hav- 
ing given the long diameter 
— Let A B be the long di- 
ameter. Find point C by 
bisecting A B. (Problem 
L) With C as a center 
and radius A C, draw a 
circle. With A as a center 
and the same radius, draw 
arcs 1 and 2, cutting the 
circle at D and E. With 
B as a center and the same 
radius, draw arcs 3 and 
4, cutting the circle at G 
and F. Lines A D, D G, 
G B, B F, F E, and E A 
will form a hexagon. 



194 



MECHANICAL DRAWING 



PROBLEM 27 




To draw a hexagon, when 
the length of one side is 
given — If A B is the given 
side, draw arcs 1 and 2 
with A and B as centers 
and radius A B. With C 
as a center, draw circle 3 
through A and B. With 
D as a center, and same 
radius, draw arc 4, cutting 
circle 3 at F. With E as 
a center and the same ra- 
dius, draw arc 5 cutting 
circle at G. Lines A D, D 
F, F G, G E, and E B are 
the required lines of the 
hexagon. 



PROBLEM 28 




To draw a hexagon, the 
short diameter being given 
— Erect the perpendiculars 
G E and D F at the ends 
of the short diameter A B. 
(Problem 4.) Find point 
C by drawing the bisector 
H K. (Problem 1.) Make 
angle BCD equal 30 de- 
grees. (Problem 25.) With 



GEOMETRICAL PROBLEMS 



195 



C as a center and a radius equal to the distance 
from C to D, draw a circle. Connecting points D H, 
H G, G E, E K, K F, and F D will give the required 
hexagon. 



PROBLEM 29 







£^ 




^ 


<^^^ 


^^^ 


^ 


1 1 


\ 


/ 




\ 


/ 


\ 


// 

1 


^ 


^^ 


^ 





To draw an octagon, hav- 
ing given the long diameter 
— Find point C by bisect- 
ing the long diameter A B. 
(Problem 1.) Draw lines 
F H and K G making 
angles of 45 degrees with 
A B. (Bisect angles BCD 
and A C D.) With C as a 
center and a radius equal 
to the distance from C to 
B draw a circle. Con- 
necting B F, F D, D K, 
K A, A H, H E, E G, and 
G B will give the required 
octagon. 



CHAPTER XVII 
GEOMETRICAL EXERCISES 

SUGGESTIONS FOR HOME WORK 

These problems may be solved in a 5x7 rectangle. 
For the home work a cheap compass, made espe- 
cially for the solution of problems in geometry and 
costing about 25 cents, may be employed. If these 
problems are inked, it is well to ink all given hnes full,- 
all results ^dth a long and short dash, and to leave 
all construction lines in pencil. Show the construc- 
tion for each problem entering into the solution of 
the exercise. 

1. Draw an oblique line Ste'^ long and bisect it. 
(Problem 1, page 181.) 

2. Bisect an arc of Stg'^ radius, having a chord of 
4^'\ (Problem 2, page 181.) 

3. Di\dde a horizontal line 4:^'^ long into four equal 
parts. (Original.) 

4. Divide the arc of a semicircle of 21'^ radius 
into four equal parts. (Original.) 

5. Locate two points 3W^ apart. Draw an arc 
through these points T\dth 3j' radius.- (Original.) 

6. Draw an oblique line 4F' long. Erect a per- 
pendicular at a point on the line 2'' from one end. 
rProblem 3, page 181.) 



GEOMETRICAL EXERCISES 197 

7. At a point Y^ from the end of and on a hori- 
zontal hne 5'^ long, erect a perpendicular to the line. 
(Problem 4, page 182.) 

8. The two parallel sides of a trapezoid measure 
24^' and 3f , respectively. These two sides are 
perpendicular to an oblique line It^'' long. Draw 
the trapezoid. (Original.) 

9. From a point at least 2^^ above and near the 
end of a horizontal line 4i'' long, draw a perpendicu- 
lar to the line. (Problem 5, page 182.) 

10. Draw a perpendicular to a horizontal line 
which is 3F' long from a point at least 2i'' from and 
over the center of the line. (Problem 6, page 183.) 

11. Two lines 21^' and 3f long, respectively, 
form a right angle. Draw the angle. (Original.) 

12. Through a point not less than 1|^' from an 
oblique line 3F' long draw a parallel to the line. 
(Problem 7, page 183.) 

13. Draw a parallelogram in which two of the sides 
shall be Sye'' long and If" apart. (Original.) 

14. Divide a line Aite" long into three equal parts. 
(Problem 8, page 184.) 

15. Draw two lines making any obtuse angle; 
copy the angle; have none of the lines horizontal 
and all at least 2i'' long. (Problem 9, page 184.) 

16. Draw any acute angle having sides at least 
2f long. Bisect the angle. (Problem 10, page 
185.) 

17. Bisect a right angle having sides at least 2rf 
long. (Original.) 

18. Draw any obtuse angle with sides at least 



198 MECHANICAL DRAWING 

2i'' long. Divide the angle into four equal parts. 
(Original.) 

19. An oblique line 2W long is the base of an 
equilateral triangle. Construct the triangle. (Prob- 
lem 11, page 186.) 

20. A vertical line 3i'' long is one side of an 
equiangular triangle. Draw the triangle. (Original.) 

21. Draw an isosceles triangle in which the base 
is a horizontal line 3A'' long and the equal sides are 
2^'\ (Problem 12, page 186.) 

22. The altitude of an isosceles triangle is 3W 
and the base is 2 J''. Draw the triangle. (Original.) 

23. Draw an isosceles triangle in which the equal 
sides are 2f long and form a right angle. (Orig- 
inal.) 

24. Construct a scalene triangle having sides 
2¥\ 3V' and 4^'. (Problem 13, page 187.) 

25. The base of a scalene triangle is 3F' long. 
One of the other sides makes a right angle with the 
base and the third side is 5i'' long. Draw the tri- 
angle. (Original.) 

26. The altitude of a triangle is 21''; the base 
is 3f long; and one of the sides is 4:W- Draw the 
triangle. (Original.) 

27. Draw a square having sides 3 A^' long. (Prob- 
lem 14, page 187.) 

28. In a rectangle the parallel sides are 3F' and 
2f , respectively. Draw the rectangle. (Original.) 

29. The three sides of a triangle measure 4f , 
3F' and 3 J''. Circumscribe a circle about this 
triangle. (Problem 15, page 188.) 



GEOMETRICAL EXERCISES 199 

30. Locate any three points and draw a circle 
through them. (OriginaL) 

31. Circumscribe a circle about a right-angled, 
scalene triangle. The base of the triangle is 3i'' and 
the altitude is 2" . (Original.) 

32. About a three inch square circumscribe a 
circle. (Problem 16, page 188.) 

33. Within a circle of Z\" diameter draw a square 
with the corners touching the circumference of the 
circle. (Original.) 

34. Inscribe a circle within a square having sides 
?>\" long. (Original.) 

35. Inscribe a circle within a right triangle having 
sides bounding the right angle which measure ^\" 
and Z\". (Problem 17, page 188.) 

36. At any point on the circumference of a circle 
34'' in diameter, draw a tangent to the circle. 
(Problem 18, page 189.) 

37. Without using the radius of the circle, draw 
a tangent to an arc of ?>\" radius. (Problem 19, 
page 189.) 

38. From a point 3f from the center of a circle 
which is Vi' in diameter, draw a tangent to the 
circle. (Problem 20, page 189.) 

39. Draw two tangents to an arc of 2f radius 
from a point M' from the center of the arc. (Origi- 
nal.) 

40. Construct any right-angled triangle the long- 
est side of which shall be W long. (See note fol- 
lowing Problem 20, page 190.) 

41. Draw two intersecting lines making any angle. 



200 MECHANICAL DRAWING 

With a radius of IJ^' draw an arc tangent to the 
two lines. (Problem 21, page 190.) 

42. Two circles of 2\" and ?i\" diameter have 
their centers ?>\" apart. With a radius of \\" , 
draw an arc tangent to the two circles. (Problem 
22, page 191.) 

43.- Draw two circles each having a radius of Ir^" 
tangent to each other and also tangent to a circle 
2\" in diameter. (Original.) 

44. Having given three circles 2W 2'^' and 3" 
in diameter, draw them so that each shall be tangent 
to the other two. (Original.) 

45. At a point \\' from one end of a line which 
is 4i'' long, erect a perpendicular. At)out a point 
on this perpendicular 2^' from the given hne draw 
a circle of \\" radius. With a radius of Y^' draw 
an arc tangent to the circle and the given straight 
line. (Problem 23, page 191.) 

46. Using the circle and the straight line described 
in Exercise 45, draw an arc of \" radius tangent to 
the circle and the straight line with its center out- 
side of the given circle. (Original.) 

47. Construct an angle of 60°, making the sides 
at least 2^' long. (Problem 24, page 192.) 

48. A vertical line 2\" long forms one side of an 
angle of 30°. Construct the angle. (Problem 25, 
page 193.) 

49. Draw an angle of 30°, without using the method 
described in Problem 25. (Combine Problem 24, 
page 192 and Problem 10, page 185.) 

50. Construct an angle of 15° with one side a 



GEOMETRICAL EXERCISES 201 

horizontal line not less than 2J'' long. (Orig- 
inal.) 

51. Draw an angle of 224°. Make sides 2i" 
long. (Original.) 

52. Construct an angle of 75°. (Original.) 

53. Draw an angle of 37i°. (Original.) 

54. The base of a right triangle is 3f long and one 
of the angles is 30°. Draw the triangle. (Original.) 

55. In an isosceles triangle the base measures 34'' 
and the equal angles are 45°. Draw the triangle. 
(Original.) 

56. The obtuse angle of a scalene triangle measures 
135° and the base is 3'' long. Draw a triangle satis- 
fying these requirements. (Original.) 

57. The angle made by the equal sides of an isos- 
celes triangle is 15° and the equal sides are 4'' long. 
Draw the triangle. (Original.) 

58. The long diameter of a hexagon is 4''. Con- 
struct the hexagon. (Problem 26, page 193.) 

59. Divide a circle of If radius into six equal 
parts. (Original.) 

60. Using a line 1^ long as one side of a hexagon, 
construct the hexagon. (Problem 27, page 194.) 

61. Draw a hexagon having a short diameter of 
31''. (Problem 28, page 194.) . 

62. Draw a polygon having a long diameter of 
3|" and twelve equal sides. (Original.) 

63. Draw an octagon with the long diameter 4i". 
(Problem 29, page 195.) 

64. Inscribe a circle within an octagon whose 
circumscribing circle is Irl" radius. (Original.) 



, 




University of 
Connecticut 

Libraries